SPS Math Diagnostic – Pre Grade 10
Contents
Operations with Whole Numbers ................................................................................................................. 2
Decimals ........................................................................................................................................................ 2
Parts of a Whole............................................................................................................................................ 3
Integers ......................................................................................................................................................... 4
Powers and Roots ......................................................................................................................................... 5
Factors and Multiples.................................................................................................................................... 5
Cartesian Plane ............................................................................................................................................. 6
Polynomials ................................................................................................................................................... 6
Patterns ......................................................................................................................................................... 7
Solving Equations .......................................................................................................................................... 9
Pythagoras .................................................................................................................................................... 9
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SPS Math Diagnostic – Pre Grade 10
Operations with Whole Numbers
1. 23 + 12 + 16
8.
195
3
2. 12 – 4
3. 36 – 17
4. 8 x 7
9. 3 + 7 x 4
10. 4 x 8 + 8  4 – 3
5. 4 x 9
6.
9
3
11. 5 + 7 x (9 – 4 + 3)
7.
56
8
Decimals
1. Use <, >, or = to make the statements true:
a) 0.6 ____ 0.8 ____ 56.5
b) 42.18 ____ 42.7
2. 2.9 + 3.2 + 1.6
6. 2.78 x 0.1
3. 7.1 – 3
7. 3 5.4
4.
$47.78
−$31.65
8. 12  0.1
5. 5000 − 122.4
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SPS Math Diagnostic – Pre Grade 10
Fractions
1. Order the following fractions from smallest to largest.
a)
7
10
4
10
3
10
8
10
b)
5
6
1
3
1
2
2
3
2. Give an example of a fraction larger than 0.5.
3.
4
7
3
+7
6.
3
5
3
×5
7. 10 ×
4.
3
5
+
1
4
1
8.
8
9
÷3
9.
2
5
÷
2
3
4
5. 4 4 − 1 3
5
6
Parts of a Whole
1. Fill in the blanks on the following chart:
Decimal
Fraction
Percent
0.25
0.8
Decimal
Fraction
2
3
5
2
Percent
1.24
50%
0.435
40%
3
100
1
25
8%
181%
2. Circle which test score is highest in percent.
a) 7 out of 10
b) 15 out of 25
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SPS Math Diagnostic – Pre Grade 10
c) 26 out of 30
d) 40 out of 50
Integers
1. Order the following sets of integers from smallest to largest -5, +9, 0, -1
2. Circle the comparison that is true.
a) -8 < -10
b) -7 > +4
c) -6 < -1
d) -3 > 0
3. (+5) + (-10)
7. (-4)(6)
4. (-6) + (-9)
8. (-2)(3)(-5)
5. (+2) – (-6)
9.
6. (-4) – (-4)
11. (−360)  (-12)
−48
6
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SPS Math Diagnostic – Pre Grade 10
Powers and Roots
1. What is the value of 70?
2. What is an equivalent expression to 58 x 56?
3. Simplify
a) 1010  105
b)
c) (𝑥 3 ∙ 𝑥 6 )2
d) (4𝑛4 )3
(−2)3
−2
4. Simplify
a) √49
b) √1.44
5. Circle which of the following is NOT a perfect square.
a) 196
b) 256
c) 476
d) 676
6. Which of the following numbers has a square root that falls between 8.2 and 9.9?
a) 9
b) 64
c) 81
d) 100
2 3
7. Evaluate (− 5)
Factors and Multiples
1. What are all of the factors of 24?
2. List all of the prime factors of 120. (you might use a factor tree here)
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SPS Math Diagnostic – Pre Grade 10
Cartesian Plane
1. Write the (x,y) coordinates for each point:
C
H
2. Which point is described by the coordinates:
(3, -1)
(-6, -1)
Polynomials
1. What is the simplified form of this expression?
4y2 – 2y + 3y – 11y2
2. Complete the addition :
(p2 + 3s + 5) + (3p2 + s + 1)
4. Complete the multiplication:
-4c (2c – 3)
3. Complete the subtraction:
(6 – 3q2 + 7r2) – (9 + 4q2 + 3r2)
5. Complete the division:
12𝑝2 − 18𝑝 + 24
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SPS Math Diagnostic – Pre Grade 10
6. With a diagram, find the side lengths of
a rectangle with an area of x2 + 5x + 6.
8. What is the product of the binomial
multiplication (z – 5)(z – 4)
7. What are the side lengths of a rectangle
with area k2 + 3k + 2
Patterns
1. How many kilometers will Cindy jog in 5
hours?
Hours
1
2
3
4
5
Kilometers
4
8
12
16
?
2. Given the following table of values,
what is an equation that describes the
pattern?
X
y
1
5
2
7
3
9
4
11
5
13
3. What is the pattern rule?
Input
46
50
18
94
Output
23
25
9
47
4. Fill in the table of values: y = 2x + 1
x
y
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SPS Math Diagnostic – Pre Grade 10
5. Sam walks toward a motion sensor at constant speed, then stops and waits a moment, then
walks backwards at a constant speed. Which graph represents Sam’s movements?
a.
c.
b.
d.
6. What is the expression for three times a number minus five?
7. Which is the correct equation for the following statement: one more than double a number is
11?
a. X + 1 = 11
b. 2x + 1 = 11
c. 2x = 11 + 1
d. X + 2x = 11
8. Study the graph below. What is the equation of the line passing through the points marked on
the graph?
12
11
10
9
8
7
6
5
4
3
2
1
0
0 1 2 3 4
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SPS Math Diagnostic – Pre Grade 10
Solving Equations
1. 𝑥 + 5 = 11
4. 3(𝑥 + 5) = 213
2. 3𝑥 = 12
5. 3𝑥 − 4 = −2𝑥 + 6
3. 2𝑥 − 3 = 15
Pythagoras
1. What is the length of the unknown side? Calculate to 1 decimal if needed.
a)
? cm
3 cm
4 cm
b)
? cm
8 cm
2 cm
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