Maths practice
Grade 8 maths
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A. Integer exponents
- A.1 Evaluate powers with positive bases
- A.2 Evaluate powers with negative bases
- A.3 Zero exponents
- A.4 Negative exponents
- A.5 Negative bases with negative exponents
- A.6 Evaluate powers with any integer exponent
- A.7 Product rule for exponents: find the exponent
- A.8 Quotient rule for exponents: find the exponent
- A.9 Power of a power: find the exponent
- A.10 Exponent laws: product, quotient and power
- A.11 Exponent laws with negative exponents
- A.12 Evaluate a product of powers with the same base
- A.13 Evaluate a quotient of powers with the same base
- A.14 Evaluate a power of a power
- A.15 Evaluate powers with a negative exponent in a product
- A.16 Write repeated multiplication as a power
- A.17 Powers of fractions
- A.18 Powers of fractions with negative exponents
B. Scientific notation
- B.1 Convert scientific notation to standard form: large numbers
- B.2 Convert scientific notation to standard form: small numbers
- B.3 Convert standard form to scientific notation: large numbers
- B.4 Convert standard form to scientific notation: small numbers
- B.5 Scientific notation in real-world measurements
- B.6 Multiply numbers in scientific notation
- B.7 Multiply decimals in scientific notation
- B.8 Divide numbers in scientific notation
- B.9 Divide in scientific notation with negative exponents
- B.10 How many times larger? Compare numbers in scientific notation
- B.11 Order numbers in scientific notation
- B.12 Order numbers in scientific notation with negative exponents
- B.13 Add numbers in scientific notation
- B.14 Subtract numbers in scientific notation
- B.15 Compare numbers in scientific notation
C. Square roots and cube roots
- C.1 Square roots of perfect squares
- C.2 Cube roots of perfect cubes
- C.3 Square roots of fractions
- C.4 Square roots of decimals
- C.5 Add, subtract and multiply square roots of perfect squares
- C.6 Solve equations with squares
- C.7 Solve equations with squares: both solutions
- C.8 Solve equations with cubes
- C.9 Solve equations with squares and fractions
- C.10 Side length of a square from its area
- C.11 Edge length of a cube from its volume
- C.12 Side of a square or edge of a cube
- C.13 Simplify square roots
- C.14 Simplify square roots with a coefficient
- C.15 Between which two whole numbers is the cube root?
- C.16 Round cube roots to the nearest whole number
- C.17 Fence around two square gardens
D. Rational and irrational numbers
- D.1 Rational or irrational: square roots
- D.2 Rational or irrational: fractions, decimals and roots
- D.3 Write repeating decimals as fractions
- D.4 Between which two whole numbers is the square root?
- D.5 Round square roots to the nearest whole number
- D.6 Round square roots to the nearest tenth
- D.7 Compare a square root with a decimal
- D.8 Order irrational numbers and decimals
E. Slope
- E.1 Slope from rise and run
- E.2 Slope from two points: positive whole-number slopes
- E.3 Slope from two points with negative slopes
- E.4 Slope from two points: fractions
- E.5 Slopes of horizontal and vertical lines
- E.6 Slope from a table: positive slopes
- E.7 Slope from a table with negative slopes
- E.8 Slope from a table: fractions
- E.9 Slope of a line from y = mx + b
- E.10 Slope of a line from y = mx + b: fractions
- E.11 Slope from the standard form of a line
- E.12 Compare unit rates: who is faster?
F. Intercepts and equations of lines
- F.1 y-intercept of a line from y = mx + b
- F.2 y-intercept of a line with fraction slope
- F.3 Slope and y-intercept together
- F.4 Slope and y-intercept with fraction slopes
- F.5 x-intercept of a line from y = mx + b
- F.6 y-intercept from the standard form of a line
- F.7 x-intercept from the standard form of a line
- F.8 Write the equation of a line from the slope and y-intercept
- F.9 Write the equation of a line from the slope and a point
- F.10 Write the equation of a line from two points
G. Functions
- G.1 Is it a function? Ordered pairs
- G.2 Evaluate a linear function
- G.3 Evaluate a quadratic function
- G.4 Find the input for a given output
- G.5 Linear or nonlinear? Tables
- G.6 Compare the rates of change of two functions
- G.7 Are two lines parallel?
- G.8 Domain of a relation
- G.9 Range of a relation
- G.10 Compare initial values of two functions
- G.11 Linear or nonlinear equations
H. Rate of change and initial value
I. Equations in one variable
J. Systems of equations
- J.1 Is an ordered pair a solution of the system?
- J.2 How many solutions does the system have?
- J.3 How many solutions? Systems in standard form
- J.4 Solve a system by substitution: both equations in slope-intercept form
- J.5 Solve a system by substitution: one equation solved for y
- J.6 Solve a system by elimination: opposite coefficients
- J.7 Solve a system by elimination: multiply one equation
- J.8 Solve a system of equations in standard form
- J.9 Systems word problems: sum and difference
- J.10 Systems word problems: wheels on bicycles and tricycles
- J.11 Systems word problems: one number is a multiple of another
- J.12 Find x in a system by setting the expressions equal
- J.13 Find y in a system by setting the expressions equal
- J.14 When do two plans cost the same?
K. Transformations
- K.1 Translate a point
- K.2 Reflect a point in the x-axis or y-axis
- K.3 Reflect a point in an axis or the line y = x
- K.4 Rotate a point 180 degrees about the origin
- K.5 Rotate a point 90 degrees about the origin
- K.6 Rotate a point 90 or 180 degrees about the origin
- K.7 Dilate a point by a whole-number scale factor
- K.8 Dilate a point by a fractional scale factor
- K.9 Find the scale factor of a dilation
- K.10 Translate then reflect or rotate a point
- K.11 Identify a translation or a reflection
- K.12 Identify a transformation: translation, reflection, rotation or dilation
- K.13 Congruent, similar or neither: compare side lengths
- K.14 Translate a triangle: find the image of a vertex
- K.15 Reflect a triangle in an axis: find the image of a vertex
- K.16 Reflect a triangle in an axis or the line y = x
- K.17 Describe a translation from two points
- K.18 Which axis was the point reflected in?
- K.19 Which rotation about the origin?
- K.20 Lengths after a dilation
- K.21 Areas after a dilation
- K.22 Find a missing side of similar triangles
L. Angles and polygons
- L.1 Corresponding angles and parallel lines
- L.2 Alternate interior angles and parallel lines
- L.3 Alternate exterior angles and parallel lines
- L.4 Vertical angles at a transversal
- L.5 Co-interior angles and parallel lines
- L.6 Angles formed by parallel lines and a transversal
- L.7 Solve for x: equal angles at a transversal
- L.8 Solve for x: co-interior angles
- L.9 Sum of the interior angles of a polygon
- L.10 Missing angle in a quadrilateral
- L.11 Missing angle in a pentagon
- L.12 Missing angle in a hexagon
- L.13 Interior angle of a regular polygon
- L.14 Interior angle of a regular polygon: round to the nearest tenth
- L.15 Exterior angle of a regular polygon
- L.16 Number of sides of a regular polygon from its angle
- L.17 Are two triangles similar? Compare angles
- L.18 Solve for x: the angles of a triangle
- L.19 Solve for x: angles on a straight line
- L.20 Number of diagonals of a polygon
- L.21 Number of sides from the sum of the interior angles
- L.22 Missing exterior angle of a polygon
M. Pythagorean theorem
- M.1 Find the hypotenuse of a right triangle
- M.2 Find a leg of a right triangle
- M.3 Find a missing side of a right triangle
- M.4 Find the hypotenuse: round to the nearest tenth
- M.5 Find a leg: round to the nearest tenth
- M.6 Find a missing side: round to the nearest tenth
- M.7 Is it a right triangle? Converse of the Pythagorean theorem
- M.8 Is it a right triangle? Sides that are close
- M.9 Distance between two points
- M.10 Distance between two points: round to the nearest tenth
- M.11 Pythagorean theorem word problems: ladders
- M.12 Pythagorean theorem word problems: diagonals of rectangles
- M.13 Diagonals of rectangles: round to the nearest tenth
- M.14 Perimetre of a right triangle from its legs
- M.15 Area of a right triangle from the hypotenuse and a leg
- M.16 Is the triangle acute, right or obtuse?
- M.17 Is it a Pythagorean triple?
- M.18 Diagonal of a box
- M.19 Hypotenuse of an isosceles right triangle
- M.20 How far from the start? East then north
N. Volume of cylinders, cones and spheres
- N.1 Volume of a cylinder
- N.2 Volume of a cylinder in terms of π
- N.3 Volume of a cylinder from its diametre
- N.4 Volume of a cylindrical tank
- N.5 Volume of a cone
- N.6 Volume of a cone in terms of π
- N.7 Volume of a sphere
- N.8 Volume of a hemisphere
- N.9 Find the height of a cylinder from its volume
- N.10 Find the height of a cylinder or cone from its volume
- N.11 Find the radius of a cylinder from its volume
- N.12 Volume of a silo: a cylinder with a cone on top
- N.13 Capacity of a cylinder in millilitres
- N.14 Surface area of a cylinder
- N.15 Volume of a cone from the matching cylinder
O. Bivariate data
- O.1 Describe the association in a scatter plot from data
- O.2 Use a line of best fit to predict
- O.3 Use a line of best fit with a decimal slope
- O.4 What the slope of a line of best fit means
- O.5 What the intercept of a line of best fit means
- O.6 Find x for a predicted y on a line of best fit
- O.7 Relative frequency in a two-way table: students who play a sport
- O.8 Relative frequency in a two-way table: students in the band
- O.9 Relative frequency in a two-way table: all students
- O.10 Spot the outlier in a scatter plot
- O.11 Percent of students from a two-way table
- O.12 Slope of a line of best fit from two points
P. Equations of lines
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Each skill comes from a printable math pack with an answer key.