Part 1 — Pre-Algebra
Questions 1–10
1
Easy
SIGN RULES: (−)×(−)=+ / (−)×(+)=−
Evaluate:
(−3) × (−4) + (−6) ÷ 2
(−3) × (−4) + (−6) ÷ 2
Many students forget: dividing a negative by a positive gives a NEGATIVE result.
Step 1: (−3)×(−4) = ? Step 2: (−6)÷2 = ? Step 3: Add them
A 9
B 15
C 9
D 6
(−3)×(−4) = 12 (negative × negative = positive) | (−6)÷2 = −3 | 12 + (−3) = 9. Answer: A.
2
Easy
ORDER: PEMDAS (Parentheses · Exponents · Multiply/Divide · Add/Subtract)
Simplify using order of operations:
5 + 3 × 22 − (8 ÷ 4)
5 + 3 × 22 − (8 ÷ 4)
Many students add 5+3 first — WRONG! Exponents and multiplication come before addition.
A 15
B 31
C 12
D 31
22=4 → 3×4=12 → 8÷4=2 → 5+12−2 = 15. Answer: A.
3
Easy
DISTRIBUTE: a(b+c) = ab + ac
Expand and simplify:
3(x + 4) − 2(x − 1)
3(x + 4) − 2(x − 1)
Watch the minus sign! −2×(−1) = +2, not −2.
Distributive Property: multiply EACH term inside the parentheses
A x + 14
B x + 14
C 5x + 10
D x + 10
3x+12 − 2x+2 = x+14. Key: −2×(−1)=+2. Answer: A or B.
4
Easy
ISOLATE x: do the SAME thing to BOTH sides
Solve for x:
2x − 5 = 11
2x − 5 = 11
Add 5 to both sides first, then divide by 2.
A x = 3
B x = 8
C x = 6
D x = 8
2x−5=11 → 2x=16 → x=8. Answer: B or D.
5
Medium
FRACTION EQUATION: multiply both sides by LCD to clear fractions
Solve for x:
x3 + 2 = x+62
x3 + 2 = x+62
Multiply BOTH sides by 6 (LCD of 3 and 2) to eliminate fractions.
LCD of 3 and 2 = 6 → multiply everything by 6
A x = 6
B x = 12
C x = 6
D x = 3
×6: 2x + 12 = 3(x+6) → 2x+12 = 3x+18 → −x=6 → x=6. Answer: A or C.
6
Easy
RATIO = part/part or part/whole · PROPORTION = two equal ratios
Proportion problem:
If 4 pencils cost $2.80, how much do 10 pencils cost?
If 4 pencils cost $2.80, how much do 10 pencils cost?
Set up: 4/2.80 = 10/x, then cross-multiply.
A $6.50
B $7.00
C $6.00
D $7.00
1 pencil = $2.80÷4 = $0.70. 10×$0.70 = $7.00. Answer: B or D.
7
Medium
PERCENT CHANGE = (change ÷ original) × 100
Percent increase:
A shirt originally costs $40. It is now sold for $52. What is the percent increase?
A shirt originally costs $40. It is now sold for $52. What is the percent increase?
Always divide by the ORIGINAL price, not the new price!
A 23%
B 30%
C 20%
D 30%
Change = 52−40 = 12. 12÷40 = 0.30 = 30%. Answer: B or D.
8
Medium
EXPONENT RULES: xa·xb=xa+b / (xa)b=xab / x0=1
Simplify:
x5 · x2 x4
x5 · x2 x4
Do NOT multiply exponents when multiplying same bases — ADD them.
A x3
B x3
C x11
D x7
x5·x2 = x7. x7÷x4 = x7−4 = x3. Answer: A or B.
9
Medium
INEQUALITY FLIP: flip the sign when multiplying/dividing by a NEGATIVE number
Solve and graph mentally:
−2x + 3 > 9
−2x + 3 > 9
When you divide both sides by −2, the > flips to <!
A x > −3
B x < −3
C x < 3
D x < −3
−2x+3>9 → −2x>6 → x<−3 (flip!). Answer: x < −3. Answer: B or D.
10
Medium
SLOPE = rise/run = (y₂−y₁)/(x₂−x₁) · RISE over RUN
Find the slope of the line passing through:
(1, 3) and (4, 9)
(1, 3) and (4, 9)
Slope = (9−3) ÷ (4−1)
Always subtract y-values first (rise), then x-values (run). Keep the same order!
A m = 2
B m = 3
C m = 12
D m = 3
m = (9−3)÷(4−1) = 6÷3 = 2. Answer: A.
Part 2 — Geometry
Questions 11–20
11
Easy
TRIANGLE ANGLES: always add up to 180°
Find the missing angle:
Sum of all 3 angles in ANY triangle = 180°. No exceptions!
A 40°
B 50°
C 60°
D 50°
180° − 55° − 75° = 50°. Answer: B or D.
12
Easy
PYTHAGOREAN: a² + b² = c² (c = hypotenuse, always LONGEST side)
Find the missing side c:
a² + b² = c² → 6² + 8² = c²
c is always the hypotenuse (longest side, opposite the right angle).
A c = 10
B c = 14
C c = 12
D c = 10
6²+8² = 36+64 = 100. 100 = 10. Answer: A or D.
13
Easy
AREA of circle = πr² · CIRCUMFERENCE = 2πr · r = radius (half of diameter)
Circle problem:
A circle has a diameter of 10. Find its area. (Use π ≈ 3.14)
A circle has a diameter of 10. Find its area. (Use π ≈ 3.14)
Diameter = 10, so radius = 5. Many students use 10 instead of 5!
Area = π × r² where r = d ÷ 2
A 31.4
B 78.5
C 314
D 78.5
r = 10÷2 = 5. Area = 3.14×5² = 3.14×25 = 78.5. Answer: B or D.
14
Easy
COMPLEMENTARY = 90° total · SUPPLEMENTARY = 180° total
Angle relationships:
Two angles are supplementary. One angle is 65°. What is the other angle?
Two angles are supplementary. One angle is 65°. What is the other angle?
Supplementary = 180°. Don't confuse with complementary (90°)!
Supplementary: angle1 + angle2 = 180°
A 25°
B 115°
C 125°
D 115°
180° − 65° = 115°. Answer: B or D.
15
Medium
PERIMETER = sum of ALL sides · AREA of rectangle = length × width
Compound shape area:
A rectangle is 10 cm long and 6 cm wide. A square with side 3 cm is cut out from a corner. What is the remaining area?
A rectangle is 10 cm long and 6 cm wide. A square with side 3 cm is cut out from a corner. What is the remaining area?
Total area − cut square area = remaining area
A 60 cm²
B 51 cm²
C 57 cm²
D 51 cm²
Rectangle: 10×6 = 60 cm². Square cut: 3×3 = 9 cm². Remaining: 60−9 = 51 cm². Answer: B or D.
16
Medium
PARALLEL LINES cut by TRANSVERSAL: alternate interior angles are EQUAL
Parallel lines & transversal:
Two parallel lines are cut by a transversal. One angle measures 70°. What is the alternate interior angle?
Two parallel lines are cut by a transversal. One angle measures 70°. What is the alternate interior angle?
Alternate interior angles are equal (Z-shape). Co-interior (same side) adds to 180°.
A 110°
B 70°
C 35°
D 70°
Alternate interior angles are always equal when lines are parallel. Answer: 70°. B or D.
17
Medium
VOLUME of rectangular prism = l × w × h · think of it as stacking layers
Volume of a box:
A rectangular box is 5 cm long, 4 cm wide, and 3 cm tall. What is its volume?
A rectangular box is 5 cm long, 4 cm wide, and 3 cm tall. What is its volume?
V = length × width × height
Don't mix up volume (cm³, three dimensions) with area (cm², two dimensions)!
A 60 cm³
B 47 cm³
C 74 cm³
D 60 cm³
V = 5×4×3 = 60 cm³. Answer: A or D.
18
Medium
SIMILAR TRIANGLES: corresponding sides have the SAME RATIO (proportion)
Similar triangles:
Triangle A has sides 3, 4, 5. Triangle B is similar with shortest side = 9. What is the longest side of Triangle B?
Triangle A has sides 3, 4, 5. Triangle B is similar with shortest side = 9. What is the longest side of Triangle B?
Find the scale factor: 9÷3 = 3. Multiply all sides by 3.
The ratio must be the SAME for all corresponding sides — it's a proportion!
A 12
B 15
C 10
D 15
Scale factor = 9÷3 = 3. Longest side of A = 5. 5×3 = 15. Answer: B or D.
19
Medium
EXTERIOR ANGLE of triangle = sum of the TWO non-adjacent interior angles
Exterior angle theorem:
x = ?
EXTERIOR angle = sum of 2 remote interior angles. Do NOT subtract from 180°.
A 60°
B 120°
C 130°
D 120°
Exterior angle = 50° + 70° = 120°. Answer: B or D.
20
Medium
MIDPOINT = average of x-coords AND average of y-coords
Coordinate geometry:
Find the midpoint of the segment connecting (2, 6) and (8, 2).
Find the midpoint of the segment connecting (2, 6) and (8, 2).
Midpoint =
(x₁+x₂2,
y₁+y₂2)
Midpoint uses ADDITION then division — not subtraction like slope!
A (5, 4)
B (3, 4)
C (6, 4)
D (5, 4)
x: (2+8)÷2 = 5. y: (6+2)÷2 = 4. Midpoint = (5, 4). Answer: A or D.