Grades 10 to 12 Math Assessment
This is a 30-minute placement quiz. Choose your grade, then answer all 20 questions. Calculators are allowed. Your results go to our teachers so we can plan your lessons.
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Grade 10 Math
Grade 11 Math
Grade 12 Math
Grade 10 Math Quiz
[Linear systems] Solve the system: x + y = 10 and x − y = 4.
x = 3, y = 7
x = 6, y = 4
x = 7, y = 3
x = 4, y = 6
[Analytic geometry] What is the midpoint of the segment from A(2, −4) to B(8, 6)?
(3, 5)
(10, 2)
(6, 10)
(5, 1)
[Expanding and factoring] Expand and simplify (x + 3)².
x² + 9
x² + 6x + 9
x² + 3x + 9
x² + 6x + 6
[Quadratic relations] What is the vertex of y = 2(x − 3)² + 5?
(−3, 5)
(3, −5)
(3, 5)
(−3, −5)
[Trigonometry] In a right triangle, the side opposite angle θ is 3 cm and the side adjacent to θ is 4 cm. What is tan θ?
4/3
3/5
4/5
3/4
[Expanding and factoring] Factor x² − 49.
(x − 7)(x + 7)
(x − 7)²
(x + 7)²
x(x − 49)
[Linear systems] Solve the system: 2x + 3y = 12 and x − y = 1.
x = 2, y = 3
x = 3, y = 2
x = 0, y = 4
x = 4, y = 3
[Analytic geometry] What is the length of the line segment from P(−1, 2) to Q(5, 10)?
10
14
100
√80
[Analytic geometry] Which line is perpendicular to y = 2x + 1 and passes through (4, 3)?
y = −(1/2)x + 5
y = 2x − 5
y = −2x + 11
y = (1/2)x + 1
[Quadratic relations] What is the equation of the axis of symmetry of y = (x − 2)(x + 6)?
x = 2
x = 4
x = −2
x = −4
[Expanding and factoring] Factor 2x² + 7x + 3.
(2x + 3)(x + 1)
(2x − 1)(x − 3)
(2x + 1)(x + 3)
(2x + 1)(x − 3)
[Trigonometry] In right triangle ABC, ∠C = 90°, ∠A = 35° and the hypotenuse AB = 12 cm. Find side BC (the side opposite ∠A) to the nearest tenth.
6.9 cm
9.8 cm
8.4 cm
20.9 cm
[Quadratic relations] A ball's height in metres is h = −5t² + 20t + 1, where t is time in seconds. What is the maximum height of the ball?
2 m
21 m
1 m
41 m
[Linear systems] Adult movie tickets cost $12 and child tickets cost $8. A group buys 10 tickets for $96 in total. How many adult tickets did they buy?
6
8
5
4
[Trigonometry] In triangle ABC, ∠A = 40°, ∠B = 75° and side a = 10 cm (opposite ∠A). Find side b (opposite ∠B) to the nearest tenth.
6.7 cm
18.8 cm
3.4 cm
15.0 cm
[Quadratic relations] For which value(s) of k does x² + kx + 9 = 0 have exactly one solution?
k = 6 or k = −6
k = 6 only
k = 3 or k = −3
k = 36 only
[Analytic geometry] Triangle ABC has vertices A(0, 0), B(6, 0) and C(2, 4). What is the equation of the median from C?
y = −x + 6
x = 2
x = 3
y = −4x + 12
[Expanding and factoring] Solve 6x² − x − 2 = 0.
x = −2/3 or x = 1/2
x = 2/3 or x = −1/2
x = 2 or x = −1
x = 3/2 or x = −2
[Trigonometry] Two sides of a triangle are 7 cm and 9 cm, and the angle between them is 50°. Find the third side to the nearest tenth.
49.0 cm
7.0 cm
14.5 cm
2.9 cm
[Linear systems] For what value of k does the system 2x + 4y = 8 and x + 2y = k have infinitely many solutions?
k = 8
k = 2
k = 4
k = 16
Total score
Grade 11 Math Quiz
[Characteristics of functions] If f(x) = 3x² − 2x + 1, what is f(−2)?
17
9
−7
41
[Exponential functions] Simplify (2³)(2⁴).
2¹²
4⁷
4¹²
2⁷
[Sequences and series] What is the 10th term of the arithmetic sequence 5, 9, 13, ...?
45
41
40
49
[Trigonometric functions] What is the exact value of cos 60°?
1/2
√3/2
√2/2
√3
[Financial applications] How much simple interest is earned on $2000 at 4% per year for 3 years?
$80.00
$2240.00
$249.73
$240.00
[Characteristics of functions] What is the domain of f(x) = √(x − 3)?
x > 3
x ≥ 3
x ≥ −3
x ≥ 0
[Characteristics of functions] What is the inverse of f(x) = 2x + 6?
f⁻¹(x) = (x + 6)/2
f⁻¹(x) = 1/(2x + 6)
f⁻¹(x) = x/2 − 6
f⁻¹(x) = (x − 6)/2
[Exponential functions] Solve 3^(x + 1) = 81.
x = 4
x = 3
x = 2
x = 27
[Trigonometric functions] What is the exact value of sin 150°?
1/2
−1/2
√3/2
−√3/2
[Sequences and series] What is the 8th term of the geometric sequence 3, 6, 12, ...?
768
384
192
24
[Financial applications] $5000 is invested at 6% per year, compounded monthly, for 4 years. What is the amount at the end?
$6312.38
$6200.00
$6352.45
$81 969.36
[Characteristics of functions] The point (4, 5) is on the graph of y = f(x). Which point must be on the graph of y = −2f(x − 3) + 1?
(1, −9)
(7, −12)
(7, 11)
(7, −9)
[Exponential functions] A bacteria population starts at 500 and doubles every 3 hours. How many bacteria are there after 12 hours?
8000
4000
16 000
2 048 000
[Trigonometric functions] What is the period of y = 3 sin(2x) + 1, in degrees?
180°
360°
720°
90°
[Sequences and series] Find the sum of the first 20 terms of the arithmetic series 2 + 5 + 8 + ...
640
1220
610
59
[Characteristics of functions] Where do f(x) = x² − 4x + 7 and g(x) = 2x − 1 intersect?
(−2, −5) and (−4, −9)
(2, 3) only
(2, 3) and (4, 7)
(1, 1) and (8, 15)
[Exponential functions] Solve 2^(2x) = 8^(x − 1).
x = 1
x = −1
x = 3
x = −3
[Trigonometric functions] Solve 2 sin θ = −√3 for 0° ≤ θ ≤ 360°.
θ = 60° or 120°
θ = 210° or 330°
θ = 120° or 240°
θ = 240° or 300°
[Financial applications] How much must be invested today at 5% per year, compounded semi-annually, to have $10 000 in 6 years?
$7462.15
$7435.56
$5568.37
$8622.97
[Sequences and series] Find the sum of the geometric series 4 + 12 + 36 + ... + 2916.
1456
8744
4372
13 120
Grade 12 Math Quiz
[Polynomial and rational functions] What is the remainder when x³ − 2x² + 5 is divided by x − 2?
−11
0
5
1
[Exponential and logarithmic functions] Evaluate log₂ 32.
16
5
6
1/5
[Rates of change and derivatives] If f(x) = 4x³ − 5x + 2, what is f′(x)?
12x² − 5x
4x² − 5
12x² − 5
12x³ − 5
[Vectors, lines and planes] What is the magnitude of the vector u = [3, −4, 12]?
11
169
13
19
[Trig functions and identities] Convert 135° to radians.
2π/3
3π/4
3π/2
5π/4
[Polynomial and rational functions] What is the vertical asymptote of f(x) = (x + 1)/(x − 4)?
x = −4
x = −1
x = 4
y = 1
[Exponential and logarithmic functions] Solve log x + log(x − 3) = 1, where log means base 10.
x = 5
x = −2
x = 5 or x = −2
x = 13/2
[Rates of change and derivatives] If f(x) = (2x + 1)⁵, what is f′(x)?
5(2x + 1)⁴
10(2x + 1)⁴
10(2x + 1)⁵
2(2x + 1)⁴
[Trig functions and identities] What is the exact value of sin(5π/3)?
√3/2
−1/2
1/2
−√3/2
[Vectors, lines and planes] Find the dot product of u = [2, −1, 3] and v = [4, 5, −2].
3
−3
19
−11
[Polynomial and rational functions] Solve x³ − 7x + 6 = 0.
x = −1, −2, 3
x = 1, −2, 3
x = 1, 6
x = 1, 2, −3
[Rates of change and derivatives] What is the slope of the tangent to y = x² − 3x at x = 4?
4
8
−1
5
[Exponential and logarithmic functions] Solve 5^x = 40. Round to two decimal places.
x = 8.00
x = 2.29
x = 0.44
x = 0.90
[Trig functions and identities] Which expression is equal to sin 2x / (1 + cos 2x)?
tan x
cot x
sin x
2 tan x
[Vectors, lines and planes] Find the angle between u = [1, 2, 2] and v = [2, −1, 2], to the nearest tenth of a degree.
26.4°
116.4°
63.6°
1.1°
[Polynomial and rational functions] Solve (x − 2)/(x + 1) ≥ 0.
x < −1 or x ≥ 2
x ≤ −1 or x ≥ 2
−1 < x ≤ 2
x ≥ 2
[Rates of change and derivatives] At what value of x does f(x) = x³ − 6x² + 9x + 1 have a local maximum?
x = 3
x = 2
x = 0
x = 1
[Trig functions and identities] Solve 2cos²x − cos x − 1 = 0 for 0 ≤ x < 2π.
x = 0, 2π/3, 4π/3
x = 0, π/3, 5π/3
x = 2π/3, 4π/3
x = π, π/3, 5π/3
[Vectors, lines and planes] What is the scalar equation of the plane through (1, 2, −1) with normal vector n = [2, −3, 4]?
2x − 3y + 4z + 8 = 0
2x − 3y + 4z − 8 = 0
2x − 3y + 4z = 0
x + 2y − z + 8 = 0
[Exponential and logarithmic functions] Solve 2^(x + 1) = 3^x. Round to two decimal places.
x = 0.63
x = 1.58
x = −1.71
x = 1.71
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