End of Year Revision Packet Mathematics-IM1 Page 1 of 33 SABIS® Proprietary SABIS ® School Network Mathematics IM1 End of Year Revision Packet Chapters 1 – 12 S4 Highlights: Identify the elements of different sets of numbers. Convert numbers from decimal form to fractional form and vice versa. Test a number for divisibility by a given prime number. Give the prime factorization of a given number using knowledge of prime and composite numbers as well as factors and multiples. Find the greatest common factor and the lowest common multiple of two numbers. Write a fraction in simplest form. Express a fraction as a mixed numeral and vice versa. Add, subtract, multiply, and divide fractions. Perform operations on directed numbers. Order directed numbers. Simplify numerical expressions. Express numbers in scientific notation, understand significant figures, and round to a nearest given value. Find the range of values of rounded numbers and find the error of given measurements. Solve a linear equation in one variable and solve word problems leading to linear equations. Solve a linear equation in more than one variable for one variable in terms of the other. Solve a linear equation involving absolute values. Solve a linear inequality in one variable and graph its solution. Solve word problems leading to linear inequalities. Solve absolute value inequalities and graph the solution. Solve word problems leading to absolute value inequalities. Solve problems involving ratios and proportions. Solve different types of questions and word problems involving percentages. Define a relation and determine its range, draw its arrow diagram, list the pairs in it, and represent it in a coordinate plane. Define a function and know that it can be represented by a rule, in a coordinate plane, or by a table. Analyze graphs of different types of functions. Recognize the general form of the rule of a linear function and graph it. Recognize nonlinear functions. Recognize an arithmetic sequence, find its common difference, apply the rule of its general term, and graph it. Use arithmetic sequences to solve problems in context.
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End of Year Revision Packet Mathematics-IM1 Page 1 of 33
SABIS® Proprietary
SABIS® School Network Mathematics
IM1
End of Year Revision Packet
Chapters 1 – 12 S4
Highlights:
Identify the elements of different sets of numbers.
Convert numbers from decimal form to fractional form and vice versa.
Test a number for divisibility by a given prime number.
Give the prime factorization of a given number using knowledge of prime and composite
numbers as well as factors and multiples.
Find the greatest common factor and the lowest common multiple of two numbers.
Write a fraction in simplest form.
Express a fraction as a mixed numeral and vice versa.
Add, subtract, multiply, and divide fractions.
Perform operations on directed numbers.
Order directed numbers.
Simplify numerical expressions.
Express numbers in scientific notation, understand significant figures, and round to a
nearest given value.
Find the range of values of rounded numbers and find the error of given measurements.
Solve a linear equation in one variable and solve word problems leading to linear equations.
Solve a linear equation in more than one variable for one variable in terms of the other.
Solve a linear equation involving absolute values.
Solve a linear inequality in one variable and graph its solution.
Solve word problems leading to linear inequalities.
Solve absolute value inequalities and graph the solution.
Solve word problems leading to absolute value inequalities.
Solve problems involving ratios and proportions.
Solve different types of questions and word problems involving percentages.
Define a relation and determine its range, draw its arrow diagram, list the pairs in it, and
represent it in a coordinate plane.
Define a function and know that it can be represented by a rule, in a coordinate plane, or by
a table.
Analyze graphs of different types of functions.
Recognize the general form of the rule of a linear function and graph it.
Recognize nonlinear functions.
Recognize an arithmetic sequence, find its common difference, apply the rule of its general
term, and graph it.
Use arithmetic sequences to solve problems in context.
End of Year Revision Packet Mathematics-IM1 Page 2 of 33
SABIS® Proprietary
Evaluate simple positive and negative powers, solve exponential equations, and evaluate
simple expressions that involve exponents.
Apply different rules related to exponents.
Recognize numbers written in scientific notation and understand what standard form is.
Apply operations on numbers written in scientific notation and solve problems involving
scientific notation.
Graph simple exponential functions, deduce one graph from the other using shifting, and
use exponential graphs to solve problems in context.
Recognize a geometric sequence, find its common ratio, apply the rule of its general term,
and graph it.
Know the general formula for compound interest and solve related problems.
Solve word problems on half-life of radioactive material.
Work out numerical expressions involving square roots.
Simplify radical expressions and express them using only one radical.
Add, subtract, multiply, and divide radical expressions.
Graph a linear equation in the coordinate plane.
Find the slope of a line.
Use the slope y-intercept form or the point-slope form to graph a line.
Identify parallel, perpendicular, intersecting, and coincident lines.
Apply the midpoint formula and the distance formula.
Check if an ordered pair is a solution of a given system of linear equations.
Solve systems of linear equations by graphing, by substitution, or by linear combination.
Graph the solution set of a linear inequality in two variables.
Graph the solution set of a system of linear inequalities.
Understand undefined terms in geometry like point, line, plane, and space.
Recognize collinear, non-collinear, coplanar, and non-coplanar points.
Define distance, segment, midpoint, and ray.
Define angle and be able to identify the interior and the exterior of an angle.
Recognize adjacent and vertical angles. Know how to measure an angle and apply the arc
addition postulate.
Solve questions about complementary and supplementary angles.
Solve questions about the bisector of an angle.
Identify alternate angles, corresponding angles, and interior angles on the same side and
apply their properties.
Define a regular polygon and know some facts about them.
Define a triangle and know its elements. Define the interior and exterior of a triangle.
Know and apply the triangle inequality.
Classify triangles by sides and angles, and know the relations between the sides and the
angles of a triangle.
End of Year Revision Packet Mathematics-IM1 Page 3 of 33
SABIS® Proprietary
Understand the distance from a point to a line geometrically and analytically.
Know and apply the angle sum theorem and the exterior angle theorem.
Define median, altitude, angle bisector, and perpendicular bisector. Know how to handle
related questions using geometric and analytic approaches.
Define congruent triangles and list corresponding parts. Know the relationships between
special lines in congruent triangles.
Know and apply the SAS postulate and the ASA, SSS, HL, and AAS theorems.
Define similar polygons and identify corresponding parts.
Define similar triangles and apply the AA postulate, SSS and SAS similarity theorems.
Know the relationships between special lines in similar triangles.
Define quadrilateral and special quadrilaterals like parallelograms, rectangles, rhombuses,
squares, and trapezoids.
Use and apply properties of special quadrilaterals using geometric and analytic approaches.
Find the perimeter and the area of a given shape in the coordinate plane.
Define a circle and congruent circles. Know all the parts of a circle. Identify the location of a
point with respect to a circle analytically.
Write the equation of a circle given the center and a point on the circle.
Define central angles and arcs. Find the arc measure and arc length.
Define locus and know the locus of points with special characteristics. Find the equation of a
given locus.
Construct geometric figures, given some properties about them. Justify their construction.
Find the image and the pre-image of a point under a translation. Find the image of a segment
and a polygon under a translation. Know that a non-trivial translation has no invariant point.
Know the relation between a point and its image under a reflection.
Find the image of a point under a reflection about a point, a vertical line, or a horizontal line.
Find the image of a polygon under a reflection.
Know the invariant points under a reflection.
Find the image of a point and a polygon after a rotation. Identify the invariant points under a
rotation.
Find the image of a point and a polygon under a given dilation. Identify the invariant points
under a dilation.
Identify the image of a point under the composite of two transformations.
Define glide translation. Identify the image of a point under two specific transformations.
Know the effect of composing a transformation and its inverse. Describe the inverse of a
reflection, rotation, dilation, or translation.
Recognize a figure with a line of symmetry or a rotational symmetry. Find the degree of
rotational symmetry of a figure.
End of Year Revision Packet Mathematics-IM1 Page 4 of 33
SABIS® Proprietary
Classify data as qualitative or quantitative.
Find the mean, mode, median, and quartiles of a set of ungrouped data.
Solve applications on the mean of a set of ungrouped data.
Find the range and the interquartile range of a set of ungrouped data.
Find the mean, median, and mode of a set of data after a linear transformation.
Find the range of a set of data after a linear transformation.
Form a frequency table for a set of ungrouped data.
Form relative and cumulative frequency table given the frequency table.
Solve applications on the cumulative frequency table.
Draw and read a line plot, a bar graph, a box-and-whisker plot, a circle graph, a histogram,
and a line graph.
Estimate using interpolation or extrapolation.
End of Year Revision Packet Mathematics-IM1 Page 5 of 33
SABIS® Proprietary
Vocabulary:
Number sets, Natural numbers, Whole numbers, Set of integers, Set of rational numbers,
Repeating decimals, Terminating decimals, Set of irrational numbers, Set of real numbers,
Divisibility, Factors, Multiples, Prime, Composite, Prime factorization, Greatest common