UTMEmaths v3.1 - My Exam Point

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UTMEMaths v3.1

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Arithmetic & Algebra part 1

QUESTION 1

Shola, Seun and Simbi are 3yrs, 6yrs and 9yrs respectively. They share 18 Oranges in theratioof their ages. How many more Oranges does Simbi get than Shola?

A. 4B. 5C. 6D. 7

Correct Answer: CExplanation

Explanation/Reference:

QUESTION 2

Evaluate correct to 4 decimal place 827.51 x 0.015

A. 11.4127 B. 12.4127 C. 11.4126 D. 12.4126

Correct Answer: BExplanation


let’s multiply: 827.51 * 0.015 = 12.41265 approximately 12.4127 (4 d.p)

QUESTION 3

Add up the following: 36527 and 6989 and leave your answer in base 10

A. 1148

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B. 1149 C. 1248 D. 1249

Correct Answer: DExplanation


QUESTION 4

Convert 3.647 to base five

A. 3.6715

B. 3.5015

C. 3.4325

D. 4.6545



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QUESTION 5

Two numbers 24x and 31y are equal in value when converted to base ten. Find the

equation connecting x and y.

A. 2x = 3(y - 1)

B. 2x = 3(y + 1)

C. 2x = -3(y - 1)

D. 2x = y

Correct Answer: AExplanation


QUESTION 6

I am x years old and my brother is 3 years older. How old was my brother last year?

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A. x + 1 B. x + 2 C. x + 3 D. x + 4



Since his/her age = x, then the bro’s age = 3+ x, bro’s age last yr = (3+ x) -1

remove the bracket: 3 + x - 1 calculate: 2 + x years

QUESTION 7

A. 2/(x + 3)

B. -2/(x + 3)

C. 3/(x + 2)

D. -3/(x + 2)



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QUESTION 8

Given that 27(1 + x) = 9, find x

A. 1/3 B. 1/6 C. -1/6 D. -1/3



QUESTION 9

A. -1 B. -3 C. 1 D. 3



QUESTION 10

(Choose two)

A. y = 7.38

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B. y = 8.43 C. y = 9.38 D. k = -10E. k = -11F. k = 11

Correct Answer: AEExplanation


QUESTION 11

A. 3 B. 4 C. 5 D. 6



QUESTION 12

A. -7 B. -3

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C. 3 D. 7



QUESTION 13

(Choose two)

A. x = -2 B. x = 1 C. x = 2 D. x = -2E. y =1F. y = 2

Correct Answer: CEExplanation


QUESTION 14

A.

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B.

C.

D.



QUESTION 15

A. 17/3 B. 5 C. 13/3 D. 4



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QUESTION 16

A. ⅓ B. ½ C. 0 D. 1



QUESTION 17

Solve the equation log2x - log2(x - 1) = 2

A. 3 B. 1⅓

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C. 1 D. no solution



QUESTION 18

A. R = T/2(TS2 - 1)

B. R = T/2(TS - 1)

C. R = T/(TS2 - 1)

D. R = 2(TS2 - 1)



QUESTION 19

A. (a + b)/(ad - bc)

B. (a - b)/(ad + bc)

C. (a - b)/(ad - bc)

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D. (b - a)/(ad - bc)



QUESTION 20

In 1984, Ike was 24 years old and his father was 45 years old. In what year was Ike exactlyhalf his father’s age?

A. 1979 B. 1980 C. 1981 D. 1982



QUESTION 21

Find x if: x + 32 - 2x = 12

A. -3 B. -1 C. 1 D. 3



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QUESTION 22

A. 2x + 3y - 7 = 0

B. 2x - 3y - 7 = 0

C. 2x + 3y + 7 = 0

D. 2x - 3y + 7 = 0



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QUESTION 23

Tosin and Bukky share apples in the ratio 2:3 respectively. If Tosin gives Bukky 5 of herapples, the new ratio of Tosin’s apples to Bukky’s becomes 1:4. How many apples does Tosin haveinitially.

A. 5 B. 10 C. 15 D. 20



QUESTION 24

A. x > 1/3

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B. x < 3/2 C. x < 1/3 D. x > 3/2



QUESTION 25

Akeem bought x apples at N6.00 each and some mangoes at N3.00 each. If he boughtthrice as many mangoes as apples and spent at least N75.00 and at most N135.00, find the range ofthe value of x.

A.

B.

C.

D.



QUESTION 26

In a racing competition Musa covered a distance of 5xkm in the first hr and (x + 10)km inthe next hr. He was second to James who covered a total distance of 118km in the two hrs.Which of the following inequalities is correct?

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A. 0 < -x < 15

B. -1 < x < 18

C. 15 < x < 18

D.



QUESTION 27

A. 2,3,4,5

B. 1,2,3,4,5

C. 2,3,4,5,6

D. 3,4,5,6



QUESTION 28

Seven years ago, the age of a father was three times that of his son, but in six years’ timethe age of the son will be half that of the father, representing the present ages of the father and

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son by x and y respectively, the two equations relating x and y are.

(Choose two)

A. 3x - x = 0

B. 3y - x = 14

C. 3y - x = 7

D. x - 2y = 6

E. 2y - x = 0

F. x - 2y = 6

Correct Answer: BFExplanation


QUESTION 29

Solve for x and y if x - y = 2 and x2 - y2 = 8 (Choose two)

A. x = 1 B. x = 2 C. x = 3D. y = 1E. y = 2F. y = 3

Correct Answer: CDExplanation


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QUESTION 30

Solve for x and y if 8x - 5y = 10 and 6x - 4y = 11

(Choose two)

A. y = -14 B. y = -7 C. y = 7 D. x = -7.5E. x = 5F. x = 7.5

Correct Answer: ADExplanation


QUESTION 31

A. 1 + 3m

B. 1 - 3m

C. 2(1 + 3m)

D. 2(1 - 3m)


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QUESTION 32

Factorize: x + y - ax - ay.

A. (1 - a)(x + y)

B. (1 - a)/(x + y)

C. (x - a)(x + y)

D. (x - a)/(x + y)



QUESTION 33

A. x = 3 or -3

B. x = 4 or 3

C. x = 3/4 or -3

D. x = 3/4 or 3



QUESTION 34

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Tunde and Shola can do a piece of work in 18 days. Tunde can do it alone in x days,while Shola takes 15 days longer to do it alone. Which of the following equations is satisfied by x?

A. x2 - 5x - 18 = 0

B. x2 - 20x + 360 = 0

C. x2 - 21x - 270 = 0

D. 2x2 + 42x - 190 = 0



QUESTION 35

Factorize abx2 + 8y - 4bx - 2axy

A. (a - 4)(bx - 2y)

B. (ax - 4)(bx - 2y)

C. (ax - 4y)(bx - 2y)

D. a(bx - 4y)



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QUESTION 36

Factorize 64x3 + 27y3

A. (4x + 3y)(16x2 - 12xy + 9y2)

B. (3x + 4y)(2x2 + 4xy + 3y2)

C. (x + 2y)(x2 - 3y2)

D. (2x - y)(8x2 - 6xy + 9y2)



QUESTION 37

The factors of 9 - (x2 - 3x - 1)2

A. -(x - 4)(x + 1)(x - 1)(x - 2)

B. (x - 4)(x - 2)(x - 2)(x + 1)

C. -(x - 2)(x + 1)(x + 2)(x + 4)

D. (x -2)(x + 1)(x + 2)(x + 1)



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QUESTION 38

Divide the expression x3 + 7x2 - x - 7 by 1 + x2

A. x + 7 rem -2x - 14

B. x - 7 rem x - 14

C. x + 5 rem -2x - 10

D. x - 5 rem x - 10



QUESTION 39

Find the values of p and q such that (x - 1) and (x - 3) are the factors of px 3 + qx2 + 11x - 6

(Choose two)

A. p = -1B. p = 1C. p = 6D. q = 1E. q = 6F. q = -6

Correct Answer: BFExplanation


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QUESTION 40

Expand the expression: (x2 - 2x - 3)(x2 + x + 1)

A. x4 - 4x2 - 5x - 3 B. -x3 - 4x2 + 5x - 3 C. x4 - x3 - 4x2 - 5x - 3 D. x4 - 4x2 - 5x - 3



QUESTION 41

When the price of egg was raised by N2 an egg, the number of eggs which can be boughtfor N120 is reduced by 5. The present price of an egg is

A. N6 B. N7 C. N8 D. N10



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QUESTION 42

Factorize a2 - b2 + (a + b)2

A. 2a2 B. 2a (a - b) C. 2a(a + b) D. 2b(b - a)



QUESTION 43

A. -3 B. -2 C. 2 D. 6



QUESTION 44

Find a positive value of p if the expression 2x2 - px + p leaves a remainder 6 when dividedby x - p

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A. 1 B. 2 C. 3 D. 4



QUESTION 45

Factorize completely the expression abx2 + 6y - 3ax - 2byx

A. (ax -2y)(bx-3)

B. (bx+ 3)(ax-2y)

C. (bx+ 3)(2y-ax)

D. (ax-2y)(ax-b)



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Aritmetic & Algebra part 2

QUESTION 1

Which of the following is represented by the below sketch?

A. y = x2 + x - 6 B. y = x2 - x - 6 C. y = x2 - x + 6 D. y = x2 + x + 6



QUESTION 2

The shaded portion in the diagram below is the solution of?

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A. y + x < 3 B. y + x > 3C. y - x < 3 D. y - x > 3



QUESTION 3

A.

B.

C.

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D.



QUESTION 4

A cubic function f(x) is specified by the graph shown above. The values of the independent variable for which the function vanishes are

A. -1, 0, 1 B.

C. x > -1D. x > 1



The graph vanishes at the region beyond x = 1 this implies: x > 1

QUESTION 5

If p varies directly as r2 and p = 3.2 when r = 4, find the value of p when r = 6.5.

A. 4.0 B. 7.5 C. 8.5 D. 9.5



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QUESTION 6

A. 80 B. 90 C. 10 D. 150



QUESTION 7

A.

B.

C.

D.



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QUESTION 8

The time taken to do a piece of work is inversely proportional to the number of menemployed. If it takes 30men to do a piece of work in 6 days, how many men are required to do the workin 4 days?

A. 35 men B. 40 men C. 45 men D. 50 men



QUESTION 9

If x varies inversely as y and y varies directly as the square root of z varies directly as 1/

w2. Write down in words how x varies with w.

A. x varies inversely as w B. x varies directly as w C. x varies directly as w2

D. x varies inversely as w2



QUESTION 10

In a restaurant, the cost of providing a particular type of food is partly constant and partly

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inversely proportional to the number of people. If the cost per head for 100 people is N30 and the cost for 40 people is N60, find the cost for 50 people.

A. N50 B. N70 C. N80 D. N100



QUESTION 11

If k + 1, 2k - 1, 3k + 1, are three consecutive terms of a geometric progression, findthe possible values of the common ratio.

A. -1, 5/3 B. 1, 5/3 C. 1 , 3 D. -1, 3



QUESTION 12

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A. 1 B. 10 C. 100 D. 1000



QUESTION 13

Find the sum of the first 18 terms of the progression 3, 6, 12, ...

A. 3(217 - 1) B. 3(218 - 1) C. 3(218 + 1) D. 3(217 + 1)



QUESTION 14

The sum of the first three terms of a geometric progression is half its sum to infinity. Findthe positive common ratio of the progression.

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A. 0.57 B. 0.68 C. 0.79 D. 0.80



QUESTION 15

Sn is the sum of the first n terms of a series given by Sn = n 2 - 1. Find the nth term.

A. -2n + 1 B. 2n + 1 C. 2n - 1 D. -2n - 1



QUESTION 16

A man’s initial salary is N540 a month and increase after each period of six months byN36 a month. Find his salary in the eight month of the third year.

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A. N828 B. N756 C. N720 D. N684




QUESTION 17

Find the nth term of the sequence 3, 6, 10, 15, 21 ...

A. n(n - 1)/2 B. n(n + 1)/2 C. (n + 1)(n + 2)/2D. n(2n + 1)




QUESTION 18

Two sets are disjoint if

A. they are both empty B. their union is an empty setC. their intersection is an empty setD. one of them is a subset of the other




QUESTION 19

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A.

B.

C.

D.



QUESTION 20

A group of market women sell at least one of yam, plantain and maize. 12 of them sellmaize, 10 sell yam and 14 sell plantain, 5 sell plantain and maize, 4 sell yam and maize, 2 sellyam and plantain only while 3 sell all the three items. How many women are in the group?

A. 25 B. 22 C. 20 D. 15


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QUESTION 21

A. {2,4,10, 12,14,16,22}

B. {4,6,12,16,20,24,28}

C. {2,10,12,22,26}

D. {2,10,14,22,26}



QUESTION 22

A. {x} B. { } C. {1,v,y} D. {x,y}



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QUESTION 23

In a class of 40 students, each student offers at least one of physics and chemistry. If the number of students that offer physics is three times the number that offer both subjects and the number that offer chemistry is twice the number that offer physics, find the number of students that offer physics only.

A. 5 B. 8 C. 12 D. 13



Let x be the number of students offering both subjectswe have number of physics to be n(P) = 3x and number of chemistry n(C) = 6x (i.e 3x * 2)

QUESTION 24

A. e = 1 B. e = -1 C. e = -2 D. e = 0



QUESTION 25

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A. 2/3 B. ½ C. -½ D. -2/3



QUESTION 26

The identity element with respect to the multiplication in the table above is

A. p B. q C. r D. s



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QUESTION 27

Which of the following binary operation is commutative in the set of integers?

A.

B.

C.

D.



QUESTION 28

A binary operation * is defined on the set of all positive integers by a *b = ab for all positive a, b. Which of the following properties does not hold?

A. Closure B. Associativity C. Identity D. Inverse



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QUESTION 29

A. -p/(p + 1) B. p/(1 - p) C. -p/(1 + p) D. p/(p - 1)



QUESTION 30

A businessman invested a total of N200,000 in two companies which paid dividends of 5% and

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7% respectively. If he received a total of N11,600 as dividend, how much did he investedat 5%?

A. N80,000 B. N120,000 C. N140,000 D. N160,000



QUESTION 31

In a class, 37 students take at least one of Chemistry, Economics and Government, 8students take Chemistry, 19 take Economics and 25 take Government. 12 students take Economics and Government but nobody takes Chemistry and Economics. How many students takeboth Chemistry and Government?

A. 3 B. 4 C. 5 D. 6



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QUESTION 32

z is partly constant and partly varies inversely as the square of d. When d = 1, z = 11 andwhen d = 2, z = 5. Find the value of z when d = 4

A. 2 B. 3.5 C. 5 D. 5.5



QUESTION 33

A. -140 B. -102 C. -67 D. 63



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QUESTION 34

A.

B.

C.

D.



QUESTION 35

A. 2 B. 3 C. 4 D. 5



QUESTION 36

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A. u = -½, B. u = 3/2C. u = -5/2D. v = 3E. v = -1F. v = 1

Correct Answer: CEExplanation


QUESTION 37

A.

B.

C.

D.



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QUESTION 38

A. 5 B. 10 C. 11 D. 23



QUESTION 39

A. 3 B. 11 C. 21 D. 22


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QUESTION 40

A.

B.

C.

D.



QUESTION 41

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A.

B.

C.

D.



QUESTION 42

A man invest $1500 for two years at compound interest. After one year, his money amountsto $1560. Find the rate of interest.

A. 2% B. 3% C. 4% D. 5%



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QUESTION 43

A rectangle whose length and breadth are 9m and 8m respectively, is mistakenly measuredas 8.8m by 7.8m. What is the percentage error in the measurement of the area of therectangle?

A. 3.78% B. 4.47% C. 5.30% D. 6.63%



QUESTION 44

A Sum of money invested at 5% per annum simple interest amounts to $285.20 after3years. How long will it take the same sum to amount to $434.00 at 7½% per annum simpleinterest?

A. 5yrs B. 7yrs C. 8yrs D. 10yrs



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QUESTION 45

The ratio of the price of a loaf of bread to the price of a packet of sugar in 1975 was r : t. In 1980 the price of a loaf went up by 25% and that of a packet of sugar by 10%. Their newratio is now

A. 40r : 50t B. 44r : 50t C. 50r : 44t D. 55r : 44t



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Geometry

QUESTION 1

A. 17° B. 23° C. 41° D. 50°



QUESTION 2

A. 30° B. 60° C. 90° D. 180°



QUESTION 3

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A. 30° B. 60° C. 90° D. 180°



QUESTION 4

A. 102° B. 120° C. 150° D. 176°



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QUESTION 5

A. 102° B. 120° C. 150° D. 176°



QUESTION 6

Each interior angle of a regular polygon is 1620. How many sides has the polygon?

A. 14 B. 17 C. 20 D. 23



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QUESTION 7

Find the number of sides of a regular polygon whose interior angle is three times theexterior angle.

A. 8 B. 9 C. 12 D. 13



QUESTION 8

The angles of a heptagon exceed one another by 15 0. Find the least angle?

A. 40° B. 56° C. 84° D. 90°



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QUESTION 9

Each interior angle of a regular polygon is 1350. How many sides has the polygon?

A. 4 B. 6 C. 8 D. 10



QUESTION 10

Find the number of sides of a regular polygon whose interior angle is twice the exteriorangle.

A. 3 B. 6 C. 8 D. 10



QUESTION 11

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A. 50° B. 70° C. 100° D. 110°



QUESTION 12

A. 24° B. 43° C. 53° D. 74°



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QUESTION 13

A. 25.5° B. 42.5° C. 62.5° D. 75.5°



QUESTION 14

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A. 62° B. 100° C. 116° D. 120°



QUESTION 15

A. 120° and 30°

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B. 105° and 45°

C. 105° and 30°

D. 120°and 45°




QUESTION 16

What is the locus of the mid-points of all chords of length 6cm within a circle of radius 5cm and with centre O?

A. A circle of radius 4cm and with centre O B. The perpendicular bisectors of the chords C. A straight line passing through centre O D. A circle of radius 6cm and with centre O



QUESTION 17

Find the equation of the locus of a point P(x,y) such that PV = PW when V = (1,1) and W =(3,5)

A. 2x + 2y = 9 B. 2x + 3y = 8 C. x + 2y = 8 D. 2x + y = 9

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QUESTION 18

The locus of a point which moves so that it is equidistant from two intersecting straightlines is the

A. Perpendicular bisector of the two lines B. Angle bisector of the lines C. Bisector of the lines D. Line parallel to the two lines




QUESTION 19

The locus of a point which is equidistant from two given fixed points is the

A. perpendicular bisector of the straight line joining themB. parallel line to the straight line joining them C. transverse to the straight line joining them D. angle bisector of 900 which the straight line joining them makes with the horizontal

Correct Answer: A

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Explanation



QUESTION 20

An arc of a circle of radius 14cm subtends angle 300 at the centre. Find the perimeter ofthe sector formed by the arc.

A. 77.41cm2 B. 83.52cm2 C. 101.33cm2 D. 108.63cm2



QUESTION 21

A. 10cm2 B. 22cm2 C. 45cm2 D. 60cm2



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QUESTION 22

A. 4cm2 B. 9cm2 C. 15cm2 D. 18cm2



QUESTION 23

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A. 50cm2 B. 72cm2 C. 98cm2 D. 104cm2



QUESTION 24

In the figure below PQR is a semi-circle. Calculate the area of the shaded region.

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A. 39.29cm2 B. 86.00cm2 C. 125.29cm2 D. 139.00cm2



QUESTION 25

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A.

B.

C.

D.



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QUESTION 26

A. 6cm2 B. 7cm2 C. 12cm2 D. 15cm2




QUESTION 27

A. 31 : 60 B. 56 : 105 C. 58 : 109 D. 62 : 113




QUESTION 28

Find the area of the shaded portion of the semi-circular figure below.

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A.

B.

C.

D.




QUESTION 29

A water tank of height ½ m has a square base of side 1½ m. If it is filled with water from a water tanker holding 1500litres, how many litres of water are left in the tanker? (1000 litres

= 1m3)

A. 125litres B. 285litres C. 375litres D. 1125litres



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QUESTION 30

A solid sphere of radius 4cm has a mass of 64kg. What will be the mass of a shell of thesame metal whose internal and external radii are 2cm and 3cm respectively?

A. 19kg B. 21kg C. 27kg D. 31kg



QUESTION 31

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A. 16cm3 B. 25cm3 C. 48cm3 D. 57cm3



QUESTION 32

P and Q are two places on the same circle of latitude 79 0 S. P is on longitude 680E while Qis on longitude 220W. The angular difference between P and Q is

A. 40° B. 70° C. 90° D. 100°



QUESTION 33

Two towns P & Q are on (40N 400W) and (40N 200E) respectively. What is the distancebetween them, along their line of latitude?

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A.

B.

C.

D.



QUESTION 34

What is the locus of points equidistant from points P(1, 3) and Q(3, 5)?

A. y = -x + 6 B. y = x + 6 C. y = -x -6 D. y = x - 6



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QUESTION 35

Which of the following lines is not parallel to the line 3y + 2x + 7 = 0?

A. 3y + 2x - 7 = 0

B. 9y + 6x +17 = 0

C. 24y +16x + 19 = 0

D. 3y -2x + 7 = 0



QUESTION 36

Find the distance of the points (½ , ½ ) and (-½, -½)

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A.

B. 2 C.

D. 5



QUESTION 37

A. 3y = -4x + 12

B. y = -4x + 11

C. y = -2x + 1

D. 3y = 2x + 7



QUESTION 38

Find the gradient of the line passing through the points P(1,1) and Q(2, 5).

A. 2

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B. 3 C. 4 D. 5




QUESTION 39

Find the equation of line parallel to y = -4x + 2 passing through (2,3).

A. 3y = -4x + 12

B. y = -4x + 11

C. y = -2x + 1

D. 3y = 2x + 7




QUESTION 40

A regular polygon has each of its angles as 160°. What is the number of sides of thepolygon?

A. 9 B. 18 C. 20 D. 36



QUESTION 41

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A cone has base radius 4cm and height 3cm. The area of its curved surface is

A.

B.

C.

D.



QUESTION 42

The interior angles of a pentagon are: 180°, 118°, 80°, 78° and x. The value of x is:

A. 75° B. 84° C. 108° D. 134°



QUESTION 43

All the vertices of an isosceles triangle lie on a circle and each of the base angles of thetriangle is 65°. The angle subtended at the centre of the circle by the base of the triangle is:

A. 130°

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B. 115° C. 100° D. 65o



QUESTION 44

A square tile measures 20cm by 20cm. How many of such tiles will cover a floor measuring5m by 4m?

A. 500 B. 400 C. 320 D. 250



QUESTION 45

The volume of a certain sphere is numerically equal to twice its surface area. The diameter

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of the sphere is:

A.

B. 6 C. 9 D. 12



QUESTION 46

A bearing of 310°, expressed as a compass bearing is:

A. N50°W B. N40°W C. S40°W D. S50°W



QUESTION 47

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A. 70° B. 90° C. 110° D. 250°



QUESTION 48

The speed of 30 kilometres per minute, expressed in centimeters per second is

A. 50 B. 500 C. 5000 D. 50000




QUESTION 49

The circle 2x2 + 2 (y - 3/2)2 = 2 has centre and radius respectively as

A. (0 , 3/2) and 2 B. (0 , -3/2) and 1 C. (3/2 , 0) and 2 D. (0 , 3/2) and 1

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QUESTION 50

The line perpendicular to the straight line y + (3/2)x - 1 = 0 has the gradient

A. -2/3 B. 3/2 C. 3 D. 2/3



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Trigonometry

QUESTION 1

Where can you get more past questions and answers on Mathematics?

A. www.jprimetutor.comB. @jprimetutorC. No whereD. [email protected]



QUESTION 2

What is our twitter handle

A. [email protected]. www.jprimetutor.comC. @jprimetutorD. www.facebook.com/jprimetutor



QUESTION 3

Our facebook page is?

A. www.jprimetutor.comB. www.facebook.com/jprimetutorC. [email protected]. @jprimetutor



QUESTION 4

What is our contact address

www.jprimetutor.com

A. [email protected]. @jprimetutorC. www.jprimetutor.comD. www.facebook.com/jprimetutor



QUESTION 5

Where can you get more past questions and answers

A. [email protected]. www.jprimetutor.comC. @jprimetutorD. like jprimetutor




QUESTION 6

When you like jprimetutor on facebook, you are supporting us

A. True

B. False




QUESTION 7

Following jprimetutor on twitter @jprimetutor will help

A. TrueB. False




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Calculus

QUESTION 1

Find the dimensions of the rectangle of greatest area which has a fixed perimeter P.

A. Square of sides P/4 B. Square of sides P/2 C. Square of sides P D. Square of sides 2P



QUESTION 2

A. 2 B. 3

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C. 3 D. 4



QUESTION 3

If y = 3t3 + 2t2 - 7t + 3 find dy/dt at t = -1

A. -5 B. -2 C. 1 D. 3



QUESTION 4

A. -5 B. -2 C. 1 D. 3



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QUESTION 5

Differentiate (2x + 5)2 (x - 4) with respect to x

A. (x + 3)(3x - 7) B. (2x + 3)(6x + 11) C. (x - 5)(5x + 7) D. (2x + 5)(6x - 11)



QUESTION 6

Obtain a maximum value of the function f(x) = x3 - 12x + 11

A. 13 B. 27 C. 30 D. 49



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QUESTION 7

If the maximum value of y = 1 + hx - 3x2 is 13, find h

A. 1 B. 2 C. 7 D. 12



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Statistics

QUESTION 1

How many three-digit numbers can be formed from 32567 without any digit being repeated?

A. 20 B. 45 C. 60 D. 120



QUESTION 2

How many possible ways are there in seating seven people P, Q, R, S, T, U and V at acircular table?

A. 60 B. 120 C. 520 D. 720



QUESTION 3

In how many ways can 6 coloured chalk be arranged if 2 are of the same colour?

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A. 72ways B. 120ways C. 360ways D. 540ways



SolutionArrangement: 6!/2! = 360 ways

QUESTION 4

A. 3 B. 7 C. 10 D. 24



QUESTION 5

In how many ways can 2 students be selected from a group of 5 students in a debating competition?

A. 10ways B. 20ways C. 120ways

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D. 200ways



QUESTION 6

A. 30 B. 45 C. 70 D. 120



QUESTION 7

A box contains black, white and red identical balls. The probability of picking a black ball at random from the box is 3/10 and the probability of picking a white ball at random is 2/5. If there are 30 balls in the box, how many of them are red?

A. 3 B. 5 C. 7 D. 9


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QUESTION 8

Find the probability that a number selected at random from 40 to 50 is a prime.

A. 2/9 B. 2/11 C. 3/9 D. 3/11



Prime numbers between 40 and 50 are 41, 43 and 47 therefore: n (prime number) = 3and there are 11 numbers from 40 to 5 therefore: p (prime numbers)= 3/11

QUESTION 9

Find the probability of selecting a figure which is a parallelogram from a square, arectangle, a rhombus, a kite and a trapezium.

A. 1/5 B. 2/5 C. 3/5 D. 4/5



Out of the 5 quadrilaterals mentioned, the parallelograms are rectangle, square andrhombus

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therefore: p(parallelogram) = 3/5

QUESTION 10

A die has four of its faces coloured white and the remaining two coloured black. What isthe probability that when the die is thrown two consecutive times, the top face will be white inboth cases

A. 2/3 B. 4/9 C. 2/9 D. 5/9



QUESTION 11

A box contains 5 blue balls, 3 red balls and 2 white balls. Two balls are selected fromthe box with replacement. Find the probability of obtaining two blue or two red balls.

A. 9/400 B. 17/50 C. 5/20 D. 9/100



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QUESTION 12

If two dice are thrown together, what is the probability of obtaining a least a score of 10?

A. 1/6 B. 1/3 C. 2/3 D. 1




QUESTION 13

Two numbers are chosen at random from three numbers 1, 3, 6. Find the probability thatthe sum of the two is not odd.

A. 1/6 B. 1/3 C. 2/3 D. 1




QUESTION 14

A bag contains 4 white balls and 6 red balls. Two balls are taken from the bag without replacement. What is the probability that they are both red?

A. 1/6 B. 1/3 C. 2/3 D. 1




QUESTION 15

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The mean of the numbers 2,5,2x, and 7 is less than or equal to 5. Find the range of value ofx.

A.

B.

C.

D.



QUESTION 16

The mean age of R men in a club is 50 years. Two men, aged 55 and 63, left the club andthe mean age reduced by 1 year. Find the value of R.

A. 20 B. 22 C. 27 D. 33



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QUESTION 17

The graph below shows the pattern of rainfall in a town in a year. What is the averagemonthly rainfall?

A. 1.13 B. 1.74 C. 2.71 D. 3.01



QUESTION 18

A. 3 B. 9 C. 11 D. 12



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Since the pass-mark is 5, students with marks less than 5 failed so, number of students that failed = 5 + 1 + 3 = 9

QUESTION 19

In a family of 21 people, the average age is 14 years. If age of the grandfather is notcounted, the average age drops to 12 years. What is the age of the grandfather?

A. 45 B. 54 C. 62 D. 87



QUESTION 20

A. 8.0g B. 12.4g C. 16.8g D. 18.6g



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QUESTION 21

A. 2 B. 3 C. 4 D. 9



QUESTION 22

A. 13.5 B. 14.5 C. 15.5 D. 16.5



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QUESTION 23

Find the standard deviation of 2, 3, 5 and 6

A. 2 B. 3/2 C. sqrt (3/2) D. sqrt (5/2)



QUESTION 24

The variance of the scores 1, 2, 3, 4, 5 is

A. 2 B. 3 C. 5 D. 8

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QUESTION 25

The cost of production of an article is made up as follows: Labour N70, Power N15, Material N30, Miscellaneous N5 find the angle of the sector representing labour in a pie chart.

A. 70° B. 120° C. 180° D. 210°



QUESTION 26

How many different three digit numbers can be formed using the integers 1 to 6 if nointeger occurs twice in a number?

A. 24 B. 48 C. 60

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D. 120



QUESTION 27

In how many different ways can the letters of the word GEOLOGY be arranged in order?

A. 720 B. 1260 C. 2520 D. 5040



QUESTION 28

A bag contains 10 balls of which 3 are red and 7 are white. Two balls are drawn atrandom. Find the probability of none of the balls is red if the draw is With replacement:

A. 0.4 B. 0.49 C. 0.9 D. 1



with replacement: Pr (none of the balls is red) = Pr(W and W) = 7/10 ´ 7/10 = 0.49

QUESTION 29

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A bag contains 10 balls of which 3 are red and 7 are white. Two balls are drawn atrandom. Find the probability of none of the balls is red if the draw is Without replacement:

A. 0.1 B. 0.21 C. 0.47 D. 0.49



without replacement: Prob(none is red) = (1 - 3/10)(1 - 3/9)therefore: 7/10 * 6/9 = 0.47

QUESTION 30

The average age of the three children in a family is 9 years. If the average age of theirparent is 39 years, the average age of the whole family is:

A. 20years B. 21 years C. 24 years D. 27 years



QUESTION 31

A bag contains 5 yellow balls, 6 green balls and 9 black balls. A ball is drawn from thebag. What is the probability that it is a black or yellow ball?

A. 37/160B. 133/400C. 77/110D. 133/800

Correct Answer: C

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Explanation


QUESTION 32

A. 64.45 B. 62.45 C. 67.45 D. 65.45



UTMEmaths v3.1 - My Exam Point

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