Non Calculator Tests Fourth Year Ppp

7/30/2019 Non Calculator Tests Fourth Year Ppp

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Non Calculator Tests

Fourth Year



Non Calculator Tests

1 2 3 4 5 6

7 8 9 10 11 12

13 14 15 16 17 18

19 20 21 22 23 24

25 26 27 28 29 30

31 32 33 34 35 36

Click on a number in the table above to go to the test of your choice.

The solutions follow after the test



Non Calculator – Test 1





Question Solutions – Test 1

1 55

2 8¾

3 4½

4 1·8

5 10·08cm2

6 0·35

7 37.67

8 4

9 37·6

10 1¼

11 10√3



1. Find 8% of £24

2. Evaluate ½ of ( 12¼ - 5¾)

3. If a = 5 , b = -3 and c = 4 find the value of b2 – 4ac

4. Evaluate 2.9 + 3.1 2

5. Factorise 9x2 – 256. Solve 5(2x-1) = 7

7. The perimeter is 32 , find x

8. Solve 2x2 = 98

9. If 5% of a number is 12 , find the number.

10. Solve the equations x + y = 13

x – y = 4

x

2x+1





1 ₤1·92

2 3¼

3 -71

4 9·1

5 (3x-5)(3x+5)

6 x = 1·2

7 x = 5

8 x = 7 or x = -7

9 240

10 x = 8.5 and y = 4.5



1. Evaluate

2. Evaluate 21.6 – 3.2 + 2.1

3. Find of ( + )

4. Write 60 as a surd in it’s simplest form. 5. Factorise fully 2x3 – 8x

6. Simplify

7. Solve 5x – 2(3x-1) > 48. Remove the brackets (2x + 3)(x2 + x + 3)

9. If sinA = ¾ and A is an acute angle , find the exact

value of cosA.

10. If y varies directly as the cube of x and x is doubled ,

find the effect on y ?

7

54

6

23

x

x x

3

1

3

2

4

1

63

168

x

x

Non Calculator- Test 3




1 x2

2 20·5

3 11/36

4 2√15

5 2x(x-2)(x+2)

6 8/3

7 x > 0·5

8 2x3 + 5x2 + 9x + 9

9 √7/4

10 multiplied by a factor of 8



1. If f(x) = 3 – 2x2 , find the value of f(-2)

2. Solve the equation 4x2 – 7x = 0

3. Factorise fully x3 – 4x4 . Simplify 45 + 20

5. Simplify the expression

6. The perimeter of a rectangle is 36 and thelength is twice the breadth.

Find the area of the rectangle.

7. Solve =

8. Find 3% of 480

9. Evaluate 2

10. Evaluate

2

25

6

23

x

x x

x

8

2

5

2

13

7

1

4

3

16





1 -5

2 x = 0 or x = 7/4

3 x(x-2)(x+2)

4 5√5

5 x9

6 72cm2

7 x = 3·2

8 14·4

9 7½

10 8



1. Find 25% of £192. If x = -2 and y = 5 find the value of +

3. If the diameter of the larger circle is

20cm and the diameter of the smaller circle is 10cm , find the shaded area.

Take as 3.

4. Subtract 6.38 from 13.95. How many pencils costing 14p

each can you buy for £5 ?

6. Change to a decimal.

7. A pupil scored in an English exam. What was his percentage mark.

8. Find the gradient of the line 2x+y+5 = 0

9. If y varies inversely as x and y=5 when x =2 find a formula connecting x and y.

Find y when x = 20.

10. If y = mx + c , change the subject of the formula to m.

x y 2 x

5

3

25

18





1 ₤4·75

2 1·5

3 225cm2

4 7·52

5 35 pencils

6 0·6

7 72%

8 m = -2

9 y=10/x ; 0·5

10 m = (y-c)/x



1. If tanx = find the exact value of cosx.

2. Write the fraction with a rational denominator in its simplest

possible form.

3. Find 5% of 42

4. Evaluate of

5. A rectangle has a length 3+2 and a breadth 3-2 .

Find an expression for the area in its simplest form.

6. Factorize 6x2 – 13x + 6

7. The perimeter of a square is 6cm. Find the area.

8. If x = 4 and y = 25 , find the value of

9. If f(x) = 3x + 5 and f(t) = 32 find the value of t

10. Solve the equation 3x2 = 5x

12

5

12

6

2

1

4

1

3

2

2

1

x 2

1

y





1 12/13

2 √3

3 2·1

4 11/24

5 7

6 (3x-2)(2x-3)

7 2·25cm2

8 2/5

9 t = 9

10 x = 0 or x = 5/3



1. Simplify

2. Simplify

3. Solve the equation 5 – 2(2x – 3) 13

4. If T = , change the subject of the formula to P

5. If x = 4 and y = 25 find the value of 26. If x + y = 17 and x – y = 4 , find the value of y.

7. If f(x) = 5x – 4 and f(t) = 11, find t.

8. Simplify 60 + 135

9. If A is an acute angle and sinA = , find the exact value of tanA.

10. Solve the equation 2x2 – 2x = 0

11. The diagram shows the graph of the function y = x2 – 4x.Find the coordinates of point P

12. Find the equation of the straight line shown.

2

34

10

45

x

x x

x x

x

52254 2

2

)31(7

4 P

2

1

2

1

y x

5

4

(0,5)(4,7) P

.





1 2x9

2 (2x+5)/x

3 x less than or equal to -0·5

4 P = (7T-124)/4

5 4/5

6 y = 6·5

7 t = 3

8 5√15

9 4/3

10 x = 0 or x = 1



1. Simplify

2. Find x as a surd in its simplest form.

3. If f(x) = 1 – 2x – x2 , find the value of f(-1).

4. If a = -3 , b = -2 and c = 5 find the value of b2 – 4ac.

5. The gradient of the line joining the points (2,5) and (5,t) is 3.

Find the value of t.

6. Find the coordinates of point T shown in the diagram

7. If x = 2 3 and y = 3 2 find the value of x2y2

8. The graph shows the relation y varies inversely

as x’ . Find the equation connecting x and y.

9. If y varies directly as the cube of

x and x is doubled, find the effect on y.

10.Solve the equations 3x + 2y = 3

y = 2x – 9

11. Factorize fully 8x4 – 2x2

12. Remove the brackets (4x – 3)( x2 – 2x – 3)

)2(3 2

1

2

1

2

1

x x x2

6

x

T

x – y = 2

x + y =10

y

x

(3,10).





1 6x - 3

2 4√2 3 2

4 64

5 t = 14

6 T(6,4)

7 216

8 y=30/x

9 y is mult by factor of 8

10 x = 3 , y = -3

11 2x2(2x-1)(2x+1)

12 4x3 - 11x2 – 6x + 9



1. What is the equation of the function shown in the diagram?

2. Factorize fully 15x2 + x – 6

3. If x = -4 , y = 2 and t = -3 find the value of yt – 2x2

4. Simplify 50 - 185. Simplify

6. Evaluate

7. If y varies directly as the square of x and x is multiplied by a factor of 3find the effect on y.

8 Find the equation of the straight line shown.

9 Write x as a surd in its simplest form.

10. Write as a single fraction

11. If , change the subject to T and hence find T when P = 40.

12. Solve the inequation -5x –7 11

4

-4

180 360

x x

x x

3

62

2

)4

3

3

2(

2

1of

y

(16,0)

(4,6)

x

3

21

2

13 x x

)13(2

1 T P





1 4cos2x

2 (5x-3)(3x+2) 3 -48

4 2√2

5 (x+2)/x

6 17/24

7 y is mult. by a factor of 9

8 y = -0.5x + 8

9 4√5 10 (5x-5)/6

11 T=(2P-1)/3 ; T = 13

12 x greater than or equal to -3.6



1 Find the equation of the straight line shown in the diagram.

2. If x = -2 find the value of 2x3.

3. Solve the equation 3x2 – 9x = 0.

4. y varies inversely as the square of x and y = 1 when x = 2.

Find a formula connecting x and y. Find y when x = 4.

5. Evaluate

6. Simplify 75 - 48

7. The perimeter of the rectangle shown is 62cm.

Make an equation and find x correct to 1 decimal place.

0

y

x

(0,3)

(6,0)

5

11

2

12

5

2x+1

Continued on next slide




8. Simplify

9. Find 4% of £48

10. Multiply out the brackets (2x – 1)3

11. Write with a rational denominator


84

4

x

12

4

1

37

20

410

x

x x




1 y=-0.5x+3

2 -16 3 x= 0 , 3

4 y=4/x2 , y = 0.25

5 3

6 √3 7 x = 7.5

8 1/(x-2)

9 ₤1·92

10 8x3 – 12x2 + 6x -1

11 √3/2

12 2x11



1. Write down the equation of the trig. function shown in the diagram.

2. If A is an acute angle and sinA = ,

find the exact value of cosA giving

your answer as a surd with a rational denominator.

3. Simplify the fraction

4. Find the exact value of cosA

5. Remove the brackets (5-3x)(6-4x)

6. If x = 36 and y = 9 find the exact value of

Non Calculator - Test 11

-3

3

90º 360º

2

1

x x

x

3

92

2

8

7

5

A

2

1

2

1

y x



7. Find x if 5x + 2y = 17 and 3x –2y = 7.

8. Find the gradient of the line shown in the diagram.

9. Simplify the expression shown

10. Find 25% of 47

11. Evaluate

12. If f(x) = and f(t) = , find t.

yx

(-5,0)

(0,-4)

)( 2

1

2

1

2

1

x x x

4

1

3

1

2

1

12

3

x

x

2

1




1 3sinx

2 √3/2

3

4 1/7

5 30 – 38x + 12x2

6 18

7 x = 3

8 m = -0·8

9 x – x-1

10 11·75

11 7/12

12 t = ¼

x

x 3



1. Identify the trig. graph shown in the diagram

2. Factorize fully 8x2 – 2y2

3. If x = -10 and y = -4 find the exact value of giving your answer

as an improper fraction in its simplest form.


5. Evaluate

6. If f(x) = 1 - 2x - 4x2 , find the value of f(-3).

-3

3

180º 360º

3

2

y

x

3

1

2

3 x x

)4

37

4

112(

2

1of




7. The area of a square is 300cm2.

Find the perimeter giving your answer as a surd in its simplest form.


9. y varies directly as the square root of x and y = 5 when x = 16.Find an equation connecting x and y. Find y when x = 9.

10. Evaluate (5x2)3

11. Solve the equation 7x – 4x2 = 0.

12. Multiply out the brackets and simplify (3 2 +1)(2 2 – 1)

(0,4)

0(12,0)




1 3sin2x

2 2(2x-y)(2x+y) 3 -25/16

4

5 2¼

6 -29

7 P = 40√3

8 m = -1/3

9 y=1.25√x ; y = 3.75

10 125x6

11 X = 0 , 7/4

12 11 - √2

6

211 x



Non Calculator - Test 13

1. The rectangle shown has an area of 84 sq.cm

Make an equation and find x.

2. Factorize fully 25t3 – t

3. Find 25% of £350

4. Simplify the expression x(x-3) – (x+2)(x+1)

5. Evaluate 13.8 – 15.6 + 4.7

6. If f(x) = 3x2 – 2x –1 , find the value of f(-2).

7. Write 500 as a surd in its simplest form.

2x+3

3



8. Find the gradient of the straight line shown.

9. y varies directly as the square of x and y = 40 when x = 2.

Find an equation connecting x and y. Find y when x = 3.

10. Evaluate (yx3)4

11. Solve the equation x2 – 6x - 16 = 0.

12. Multiply out the brackets and simplify ( 2 +1)( 2 – 1)

(0,5)

0(10,0)




1 x = 12·5

2 t(5t-1)(5t+1)

3 ₤87·50

4 -6x -2

5 2·9

6 15

7 10√5

8 m = -½

9 y = 10x2 , y = 90

10 y4x12

11 x = 8 , -2

12 1

Non Calculator Test 14




1. If sinx = , find the exact value of cosx.

2. Write the fraction with a rational denominator in its simplest possible form.

3. Find 9% of 36

4. If f(x) = 3x – 5 and f(t) = 22 , find t.

5. A rectangle has a length 5+6 and a breadth 5-6 .

Find an expression for the perimeter in its simplest form.

6. Factorise 9x2 – 12x + 4


8. If x + y = 24 and y = 2x , find the value of y

9. Simplify

10. Solve the equation x2 = 3x

186

13

5

2010

189

x

x




1 12/13 2 √2

3 ₤3·24

4 t = 9

5 20

6 (3x-2)(3x-2)

7 12·25

8 16 9 9/10

10 x = 0 , 3

N C l l t T t 15




1. Simplify

2. Simplify

3. Solve the equation 5x – (2x – 3) 1

4. If W = , change the subject of the formula to M.

5. If x = 9 and y = 16 find the value of

6. Find the V.A.T. on an article costing £400.

7. If f(x) = 5x – 1 and f(t) = -6 , find t.

1

52

20

45

x

x x

x x

x

5

252

2

)2(2

1 M

2

1

2

1

y x



8. Simplify 20 + 45

9. If A is an acute angle and sinA = , find the exact value of tanA.

10. Solve the equation 2x2 + 5x = 0

11. The diagram shows the graph of the function y = x2 – 6x.

Find the coordinates of point P, the minimum value of the function.


2

1

P

(0,1)

(10,2)




1 x8

2 3

4 M = 2W - 2

5 ¾

6 ₤70

7 t = -1

8 5√5

9 10 x = 0 or x = -5/2

11 (3,-9)

12 y = 0.1x + 1

x

x 5

x3

2

3

1




1. Find 3% of £78

2. Evaluate

3. If a = 2 , b = -1 and c = 3 find the value of ab – bc

4. Evaluate 12 4 + 6 2

5. Factorise fully 2x2 – 3x + 1

6. Simplify the algebraic fraction

7. Write 56% as a fraction in its simplest form.

8. Solve the equation 2x2 + 5x = 0

9. If 10% of a number is 17 , find the number.

10. Find the value of x if x + y = 12 and x – y = 11

11. y varies inversely as x and y = 6 when x = 5. Find y when x = 10.

5

1

3

1

2

1

34

92

2

x x

x




1 ₤2·34

2 19/30 3 1

4 15

5 (2x-1)(x-1)

6 (x-3)/(x+1)

7 14/25

8 x = 0 or x = -5/2

9 170 10 x = 11·5

11 y = 3




1. Evaluate

2. Evaluate 1.6 – 3.2 + 2.1


4. Write 80 as a surd in it’s simplest form

5. Factorize fully 6x2 – 13x + 6

6. Find the gradient of the line which

passes through the points (0,4) and (4,0)

7. Solve 6x – (3x+2) < 4

8. Remove the brackets (x + 1)(x2 + x - 3)

9. If sinA = , and A is an acute angle , find the exact value of tanA.

10. If y varies directly as the square of x and x is trebled ,

find the effect on y ?

2

63

x

x x

4

1

3

12

x x

3

2




1 x11

2 0·5 3 (5x+7)/12

4 4√5

5 (3x-2)(2x-3)

6 m = -1

7 x < 2

8 x3 + 2x2 – 3x - 3

9 2/√5 10 y is mult. by a factor of 9




1. Write the number 32.6904 correct to

a) 1 decimal place b) 5 significant figures


possible form.

3. Find 50% of 6.42

4. If f(x) = 1-2x and f(t) = 5 , find t.

5. Factorize fully 4x3 – 4x

6. Make x the subject of the formula y = mx + c.

7. The area of a square is 400cm2. Find the perimeter.

8. If x = 4 and y = 16, find the value of

9. Simplify (x+1)2 – x(x-2)

10. Solve the equation 5 – 2(x-2) = 0

18

12

2

3

x 2

1

y




1 a) 32·7 b) 32·690

2 2√2 3 3·21

4 t = -2

5 4x(x-1)(x+1)

6 x = (y-c)/m

7 P = 80

8 ½

9 4x + 1 10 x = 4·5




1. Simplify


3. If f(x) = x – x2 , find the value of f(-2).

4. Find 9% of £44

5. The gradient of the line joining the points (0,2) and (2,t) is 4.

Find the value of t.6. Write 40% as a fraction in its simplest form.

7. If x = 4 3 and y = 3 3 find the value of 2xy

8. Solve the inequation 4x – 2(1-2x) > 5

9. If y varies directly as the square of x and x is doubled, find the effect on y

10. Solve the equations 3x + 2y = 16 , y = x – 2

11. Factorize fully x4 – 81

12. Remove the brackets (x – 3)(2x2 – 2x + 3)

48

x

)2(2 2

1

2

1

2

3

x x x




1 2x2 – 4x

2 4√3 3 -6

4 ₤3·96

5 t = 10

6 2/5

7 72

8 x>7/8

9 y is mult. by 4 10 x = 2

11 (x-3)(x+3)(x2+9)

12 2x3 – 8x2 + 9x - 9

N C l l t T t 20




1. Find the equation of the straight line with a gradient

3 which passes through the origin.

2. If x = -2, find the value of 3x2.

3. Solve the equation x2 + x = 0.

4. y varies inversely as the square of x and y = 2 when x = 2.


5. Evaluate

6. Simplify 125 + 75



5

31

4

12

4

x+6



8. Simplify

9. Find 2% of £48.50

10.Multiply out the brackets (x + 2)3

11. Write in its simplest form with a rational denominator


42

2

x

8

2

2

36

16

420

x

x x



5

33


1 y = 3x

2 12

3 x = 0 or x = -1

4 y=8/x2 ; y = ½

5

6 5(√5 + √3) 7 x = 25

8 1/(x-2)

9 ₤0·97 10 x3+ 6x2 + 12x + 8

11 √2/2

12 5x11

Non Calculator 21



Non Calculator 21

1. Find 10% of £19

2. If x = -1 and y = -2 find the value of +

3. Solve the equation x2 = 3x.

4. Subtract 4.8 from 7.3

5. Remove the brackets (x + 2) (x2 + x + 1)


7. Simplify

8. Find the gradient of the line 2x+4y+1 = 0

9. If y varies inversely as the square of x and y=2 when x =3

find a formula connecting x and y. Find y when x = 6.

10. If C = , change the subject of the formula to F.

x

y 3 x

63

42

x

x

)32(9

5 F




1 ₤0·19

2 1 3 x = 0 , 3

4 2·5

5 x3+3x2 + 3x + 2

6 2/25

7 2/3

8 m = -½

9 x = 6 and y = ½ 10

5

)1609(

C F





1. If sinx = and x is an acute angle, find the exact value of cosx.


possible form.

3. Find 2% of 80

4. Evaluate of

5. A rectangle has a length 32 and a breadth 52

Find an expression for the area in its simplest form.

6. Factorise x2 – x – 6


8. If x = 9 and y = 4 , find the value of 4

9. If f(x) = 2x + 5 and f(t) = 23, find the value of t.

10. Solve the equation x2 = 5x + 4

17

8

186

41

41

21

2

1

x 2

1

y




1 15/17

2 √2

3 2

4 3/16

5 30 6 (x-3)(x+2)

7 6·25cm2

8 6

9 t = 9

10 x = 4 , x = 1





1. Evaluate

2. Evaluate 11.6 – 13.2 + 2.5

3. Remove the brackets (x + 2)(2x2 –x -1)

4. Calculate the gradient of the line which passes

through the points (5,2) and (-3,2).

5. If f(x) = 3 – x – x2, find the value of f(-3).

6. Simplify

7 . Solve the equation x2 = 7x

8 . Simplify √45 + √20 - √125

9 . If P = 4(L + B), change the subject of the formula to B.

10 . If y varies inversely as the square of x and x is doubled,

find the effect on y?

7

45

6

12

x

x x

1

2

x

x x




1 2x2

2 0·9 3 2x3 + 3x2 – 3x -2

4 m = 0

5 -3

6 x

7 x = 0 , x = 7

8 0

9 B=(P-4L)/4 10 y is divided by a factor of 4

Non Calculator – Test 24 6




1. Write down the equation of

the trig. function shown in the diagram.

2. If A is an acute angle and sinA = , find the exact

value of tanA, giving your

answer as a surd with a rational denominator.

3. Simplify the expression 2x(x+1) – (2x+1)(x-1)

4. Find the exact value of cosA.

5. Solve the equation

6. If x = 25 and y = 4, find the exact value of x -½ y ½

360º

-6

6

90º

3

2

4

5

2

A

4

3

5

12

x

x



7. Solve 2x + 3y = 21 , y = 3x – 4

8. Find the equation of the line shown in the diagram.

9. Simplify the expression shown

4

10. Find 15% of 20

11. Evaluate

12. Write √120 as a surd in its simplest form.

y

x (-2,0)

(0,-1)

)( 2

1

2

1

2

1

x x x

4

3

3

2

4

1




1 6sinx

2 2/√5 3 3x + 1

4 37/40

5 x = -3·8

6 2/5

7 x = 3 , y = 5

8 y = -0·5x - 1

9 4 – 4x 10 3

11 3/4

12 2√30





1. Find 5% of £60000

2. Evaluate ¼ of ( 10½ - 4)

3. A square has an area of 400 cm2. Find the perimeter of the square.

4. Evaluate 1.52 + 2.52

5. Factorize fully x3 – x

6. Solve 4 – 2(x – 1) = 9

7. If f(x) = x2 + 1 find the value of f(-2) – f(2).

8. Write as a surd with a rational denominator

9. A discount of 40% is offered on a television set in a

sale. Find the sale price of the set.

10. State the gradient of the line with equation x + 4y = 1

20

8




1 ₤3000

2

3 80cm

4 8·5

5 x(x-1)(x+1) 6 x = -1·5

7 0

8 4√5/5

9 Needs a price for the set.

10 -¼

16

91




1. Simplify

Find the value of this expression when x = 4.

2. Find x as a surd in its simplest form

3. If f(x) = 10 – x – x3 , find the value of f(-1).

4. y varies directly as x and y =6 when x = 4. Find y when x = 10.

5. Solve the equation x3 – 4x = 0

6. Find the coordinates of point

)5.0(8 2

1

2

1

2

1

x x x

2

8

x

P

x – y = 1

x + y = 8

y

x



7. If x = 4 2 and y = 5 2 find the value of x3y

8. The graph shows the relation y varies inversely as the square of xFind the equation connecting x and y

9. If x = 4, find the value of √(x2 + 48)

10. Find the point where the line 2x + 3y -12 = 0 cuts the x axis

11. Factorize fully x2 – x – 12

12. Remove the brackets (x – 3)( x2 – 2x + 3)

(2,5)

Q ti S l ti T t 26




1 4x - 8

2 2√15

3 12

4 y = 1·5x ; y =15

5 x = 0,2,-2

6 P(4.5,3.5) 7 1280

8 y=20/x2

9 8

10 (6,0)

11 (x-4)(x+3)

12 x3 - 5x2 + 9x - 9




1. Simplify

2. Simplify

3. Solve the equation 15 – (2x – 3) 1

4. If M = , change the subject of the formula to T


6. If 2x + y = 11 and x – y = 4 , find the value of y.

7. If f(x) = x2 – 4 and f(t) = 32, find t.

1

34

10

25

x

x x

5625

2

2

x x

x

)12(3

2

T

3

1

5

12

x x



8. Simplify 242 - 98

9. If A is an acute angle and cosA = ,

find the exact value of tanA.

10. Solve the equation x2 – 11x = 0

11. The diagram shows the graph of the

function y = x2 – 6x. Find the coordinates

of point P

12. Find the gradient of the straight line

shown.

13

12

P

6

(0,3)(5,9)

Q ti S l ti T t 27



1

5

x

x

2

243

M T

15

2 x

12

5

tan

A

5

6


1 x8

2

3 x 8.5

4

5

6 y = 1

7 t = 6 , -6

8 4√2

9 10 x = 0 , 11

11 (3,-9)

12




1. Find 5% of £1800

2. If x = -2 and y = -4 , find the value of +

3. A straight line has equation 4x + 3y = 24.

Find the point where the line cuts the y axis.

4. Subtract 4.76 from 12.38

5. Simplify the algebraic fraction

6. Change to a decimal.

x

y2 3 x

6020

3010

x

x

5

2



7. A pupil scored in a Mathematics exam.

What was his percentage mark?

8. If f(x) = ax2 + 5 and f(2) = 33, find the value of a.

9. If y varies inversely as the cube of x and y = 1 when x =2.


10. If e = mc2 , change the subject of the formula to c.

40

28



3

8

x y

m

eC


1 90

2 -4 3 (0,8)

4 7·62

5 ½

6 0·4

7 70%

8 a = 7

9 , x = 1 , y = 8 10




1. Find the equation of the straight line shown in the diagram.

2. If x = -1, find the value of x3 – x2

3. Solve the equation 4x2 – 81 = 0.

4. P varies directly as the square of Q and P = 1 when Q = 2.

Find a formula connecting P and Q.

Find P when Q = 10.

5. Evaluate

6. Simplify 200 - 128

0

y

x

(0,4)

(8,0)

311

214





8. Evaluate , when x = 2

9. Evaluate 100 – 25 5

10. Multiply out the brackets (1-3x)(4x+1)

11. Write with a rational denominator


6

3x+4

85

2

x

12

4

2

3

2 x

x




1 m = -½

2 -2 3 9/2 and -9/2

4 P=¼Q2 , P = 25

5 6

6 2√2

7 x = 6

8 1

9 -25 10 1 + x – 12x2

11 4(√2 – 1)

12 ½x5




1. What is the equation of the function shown

in the diagram?

2. If f(x) = 4 + ax3 and f(-1) = 5 , find a formula for f(x)

and hence find the value of f(3)

3. If x = 10 , y = -2 and t = 3, find the value of

4. Simplify 3x4 (2x2)3

5. Simplify

6. Evaluate

7. If x + y = 20 and y = 4x , find the value of y.

-12

360 180

t

y x

x x

x x

3

62

2

)4

7

4

3(

4

1of

y




9. Write x as a surd in its

simplest form.

10. Evaluate 23.2 – 34.7 + 16.8

11. If , change the subject to M and hence find M when L=10.

12. Solve the inequation -2x +9 5

y

(5,0)

(1,3)

x

4

x

6

)53(2

3 M L

Question Solutions Test 30




1 12cos2x

2 a = -1; f(3)=-23

3 4

4 24x10

5 (x-2)/x

6 5/8

7 x = 4 , y = 16

8 y = -0.75x + 3.75

9 x = 2√5 10 5·3

11 M=(2L-15)/9

12 x 2




1. The rectangle shown has an area of 72 sq.cm

Make an equation and find.

2. Factorize fully 121x4 – x2

3. Find 8% of £300.

4. Simplify the expression 2x(x-3) – (x+2)(2x+3)

5. Evaluate 1.42

6. A Doctor has been given a pay rise of 25%.

He now earns ₤60000 per annum.How much did he earn before the pay rise.

4x

2x

7 Write 800 as a surd in its simplest form





9. If x = √5 + 2 and y = √5 – 2, find the value of x2 + y2.

10. Evaluate √(122 + 52)

11. Solve the equation 121 – x2 = 0

12.Multiply out the brackets and simplify

(3 7 +1)( 7 – 1)

(0,6)

0(12,0)




Q

1 x =3

2 x2(11x-1)(11x+1)

3 ₤24

4 -13x - 6

5 1·96

6 48000 7 20√2

8 m = -½

9 18

10 13

11 x = 11 , -11

12 20 - 2√7




1. A straight line passes through the points (2,0) and (0,-2).

Find its equation.

2. Solve the equation Give your answer correct to1 decimal place

3. Factorize fully 4x2 – 15x + 9

4. y varies inversely as the square of x and x is doubled.

Find the effect on y.

5. Evaluate

6. Simplify 32 - 18

11

31

4

32

32

43 x

7 Th i t f th t l h i 50





8. Simplify

9 Find 3% of £1000

10. If x = -5, y= 4 and t = -2 , find the value of x2yt.

11. Write in its simplest form with a rational denominator.

12. Simplify the expression (x+1)2 – x(x+1)

5

2x+1

816

8

x

12

6





1 y = x - 2

2 x = 0·9

3 (4x-3)(x-3)

4 y is divided by 4

5 3½

6 √2 7 x = 9·5

8 1/(2x-1)

9 ₤30

10 -200

11 √3

12 x + 1




1 Evaluate

2. Simplify the expression -4x(x-1) – 4x(1-x) 3



5. Factorize fully x2 – 16x + 64

6. The point (t,5) lies on the line x + y - 9 =0. Find the value of t.

7. Solve the inequation 5x – (3x-2) < - 4

8. Remove the brackets (2x + 1)(x2 - x - 10)

9. A car costs ₤24000. In a sale it is reduced by 20%.Find the sale price of the car.

10 A car travels a distance of 250 km in 2½ hours.

Calculate the average speed of the car in km per hour.

1

52

y

y y

5

1

3

x x

Q i S l i T 33




1 y8

2 0 3 (2x+3)/15

4 6√2

5 (x-8)(x-8)

6 t = 4

7 x < -3

8 2x3 – x2 – 21x - 10

9 ₤19200 10 100km/hr




1. Simplify


3. If P = 2(L+B), change the subject to L.

4. Find of 75

5. State the gradient of the line with gradient y = 4.


7. If x = 4 3 and y = 3 3 find the value of xy2

8. Solve the equation x(x+1) = x2 + 10x + 18

9. The point (4,2) lies on the curve with equationFind the equation of the curve.

10. Evaluate 8.4 – 11.2 – (-7.8)

11. Factorize fully x4 – 9x2

12. Remove the brackets (x + 1)(x2 – x - 3)

)( 222 x x x

510

x

5

3

2 x

a

y




2

32

x


1 1 – 1/x

2 5√3

3 L=(P-2B)/2

4 45

5 m = 0

6 3/5

7 108√3

8 x = -2

9

10 5

11 x2(x+3)(x-3)

12 x3 – 4x - 3




1. The rectangle shown has a perimeter of 70 cm.


2. Factorize fully 8x2 +2x – 15

3. Find 75% of £360



6. If f(x) = x2

– 5x –6 , find the value of f(-3).

7. Write as a surd in its simplest form with a rational denominator.

2x+5

x

x x x

636

2

2

1

34

x x

20

12




9. y varies directly as the cube of x and y = 64 when x = 4.

Find an equation connecting x and y. Find y when x = 6.

10. Simplify (2y3x4)3

11. Solve the equation x2 = 6x

12. Multiply out the brackets and simplify(3 2 +1)(2 2 + 1)

(0,6)

0(16,0)




x

x 6

)1(

4

x x

x

Q

1 x = 10

2 (4x-5)(2x+3)

3 ₤270

4

5

6 18

7 6√5/5

8 -3/8

9 y = x3 , y = 216

10 8y9x12

11 x = 0 , 6

12 13 + 5√2

1.5




1. Write down the equation

of the trig. function shown in the diagram.

2. If A is an acute angle and tanA = ,

find the exact value of cosA , giving your answer as a

surd with a rational denominator.

3. Simplify the fraction

4. Find the exact value of cosA in the diagram shown.

5. If f(x) = x3 -7 and f(t) = 57, find t.

6. If x = 49 and y = 9 , find the exact value of

360º

-1.5

5

90º

3

1

x x x2

2

5

6

4 A

2

3

2

1

y x

7 Find x if x + y = 17 and x – y = 8



7. Find x if x + y = 17 and x y = 8.

8. Find the equation of the line shown in the diagram.

9. Simplify the expression shown . Henceevaluate this expression when x = 3.

10. Find 125% of 40

11. Evaluate

12. If f(x) = and f(t) = , find t.

y

x (-2,0)

(0,-1)

)24( 2

1

2

1

2

1

x x x

7

1

3

12

2

11

1 x

x2

1




6

51

Q

1 1.5sinx

2 3/√10

3 x/(x+1)

4 1/8

5 t = 4

6 189 7 x = 12·5

8 y = -0·5x - 1

9 4x – 2 ; 10

10 50

11

12 t 1

Non Calculator Tests Fourth Year Ppp

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