Q01
ORDER OF OPERATIONS · PEMDAS
Order of Operations
Evaluate:
3 + 4 × (2² − 1)
💡 Memory Point
PEMDAS → Parentheses → Exponents → Multiply/Divide → Add/Subtract
Always do what's
inside parentheses first, then exponents, then left-to-right ×÷, then left-to-right +−.
Tricky trap: many students add 3+4 first → wrong! Multiply comes before add.
A 21B 15C 27D 35
📖 Step-by-Step Solution
Step 1: Exponent inside parentheses → 2² = 4
Step 2: Subtract inside parentheses → 4 − 1 = 3
Step 3: Multiply → 4 × 3 = 12
Step 4: Add → 3 + 12 =
15
Common mistake: doing 3+4 first gives 7×3=21. Remember: × before + always!
Q02
VARIABLES · SUBSTITUTION
Algebraic Substitution
If x = −3 , what is the value of 2x² − 5x + 1 ?
💡 Memory Point
SUBSTITUTE & SQUARE FIRST : When x is negative,
always put it in parentheses: (−3)² = 9, not −3² = −9.
Rule: (−n)² =
positive
A −2B 4C 34D −16
📖 Step-by-Step Solution
Substitute x = −3:
2(−3)² − 5(−3) + 1
= 2(9) − (−15) + 1
= 18 + 15 + 1
=
34
Key trap: −5×(−3) = +15 (negative × negative = positive!)
Q03
FRACTIONS · LCM
Adding Fractions
Simplify: 5/6 + 7/9
💡 Memory Point
LCD = LCM of denominators . LCM(6,9): list multiples → 6,12,18 | 9,18 → LCD = 18.
Convert both fractions to 18ths, then add numerators.
A 12/15B 29/18C 2/3D 4/5
📖 Step-by-Step Solution
LCD of 6 and 9 = 18
5/6 = 15/18
7/9 = 14/18
15/18 + 14/18 = 29/18
29/18 is already in lowest terms (GCF of 29 and 18 is 1). Answer:
29/18
Q04
INTEGERS · SIGN RULES
Integer Operations
Calculate: (−4) × (−3) − (−2) × 5
💡 Memory Point
SIGN RULE : (−)(−) = (+) | (−)(+) = (−) | (+)(+) = (+)
Think: "Same signs → Positive. Different signs → Negative."
A −2B 2C −22D 22
📖 Step-by-Step Solution
Step 1: (−4)×(−3) = +12 (same signs → positive)
Step 2: (−2)×5 = −10 (different signs → negative)
Step 3: 12 − (−10) = 12 + 10 =
22
Trap: subtracting a negative → it becomes addition!
Q05
ONE-STEP EQUATION
Solving Equations
Solve for x :
3x − 7 = 2x + 5
💡 Memory Point
BALANCE METHOD : Whatever you do to one side, do to the other.
Goal: Get all x-terms on one side, all numbers on the other.
A x = 12B x = −12C x = 2D x = −2
📖 Step-by-Step Solution
3x − 7 = 2x + 5
Subtract 2x from both sides: x − 7 = 5
Add 7 to both sides: x =
12
Check: 3(12)−7 = 29, 2(12)+5 = 29 ✓
Q06
RATIO & PROPORTION
Ratios & Proportions
A recipe uses 3 cups of flour for every 2 cups of sugar. How many cups of flour are needed if you use 7 cups of sugar ?
💡 Memory Point
CROSS-MULTIPLY : Set up proportion: 3/2 = x/7
Cross multiply: 2x = 21 → x = 10.5
A 9 cupsB 9.5 cupsC 10.5 cupsD 14 cups
📖 Step-by-Step Solution
Set up proportion: flour/sugar = 3/2 = x/7
Cross multiply: 2x = 3 × 7 = 21
Divide: x = 21/2 =
10.5 cups
Q07
PERCENT · % CHANGE
Percentages
A shirt originally costs $40 . It is marked up 25%, then discounted 20%. What is the final price ?
💡 Memory Point
MULTIPLY MULTIPLIERS : +25% means × 1.25 | −20% means × 0.80
Don't just add/subtract the percents! 25% − 20% ≠ 5% increase.
A $42B $40C $38D $44
📖 Step-by-Step Solution
After 25% markup: $40 × 1.25 = $50
After 20% discount: $50 × 0.80 =
$40
Surprising result: back to the original price! But note: a 25% up then 20% down is NOT the same as 5% up — it depends on the base.
Q08
EXPONENT RULES
Exponents
Simplify: x³ × x⁻⁵ × x²
💡 Memory Point
SAME BASE → ADD EXPONENTS : xᵃ × xᵇ = x^(a+b)
Negative exponent means reciprocal: x⁻ⁿ = 1/xⁿ
A x⁰ = 1B x¹⁰C x⁻⁶D 3x
📖 Step-by-Step Solution
Add all exponents: 3 + (−5) + 2 = 0
x⁰ =
1 (any nonzero number to the power 0 = 1)
Trap: students multiply exponents (3×−5×2 = −30) — wrong! Same base → ADD exponents.
Q09
INEQUALITIES · FLIP RULE
Inequalities
Solve and identify the correct solution set:
−3x + 6 > 15
💡 Memory Point
FLIP the inequality when dividing/multiplying by NEGATIVE!
−3x > 9 → divide both sides by −3 → x < −3 (sign flips!)
A x > −3B x > 3C x < −3D x < 3
📖 Step-by-Step Solution
−3x + 6 > 15
Subtract 6: −3x > 9
Divide by −3 (⚠️ FLIP the sign!): x < −3
Check: try x = −4: −3(−4)+6 = 18 > 15 ✓
Try x = 0: −3(0)+6 = 6 > 15? ✗ Correct, x=0 is not a solution.
Q10
WORD PROBLEM · SYSTEM
Word Problems
Together, Sam and Alex have $54 . Sam has $6 more than twice Alex's amount. How much does Alex have?
💡 Memory Point
DEFINE → EQUATION → SOLVE : Let Alex = a. Then Sam = 2a + 6.
"Together" means add them: a + (2a + 6) = 54
A $14B $16C $18D $20
📖 Step-by-Step Solution
Let Alex = a, Sam = 2a + 6
a + 2a + 6 = 54
3a + 6 = 54
3a = 48
a =
$16
Check: Alex=$16, Sam=2(16)+6=$38. Total: 16+38=54 ✓
G01
TRIANGLE · ANGLE SUM
Triangles
In a triangle, two angles measure 47° and 68° . What is the third angle ?
💡 Memory Point
TRIANGLE SUM = 180° — always, no exceptions.
Third angle = 180 − (sum of other two angles)
A 55°B 60°C 65°D 70°
📖 Step-by-Step Solution
Sum of all angles = 180°
Third angle = 180° − 47° − 68° =
65°
G02
AREA · RECTANGLE vs SQUARE
Area & Perimeter
A rectangular garden has a perimeter of 34 m and a width of 7 m . What is its area ?
💡 Memory Point
PERIMETER of rectangle = 2(l + w)
Step 1: find the length from perimeter. Step 2: Area = l × w
A 80 m²B 70 m²C 119 m²D 60 m²
📖 Step-by-Step Solution
P = 2(l + w) → 34 = 2(l + 7)
17 = l + 7 → l = 10 m
Area = l × w = 10 × 7 =
70 m²
G03
PYTHAGOREAN THEOREM
Right Triangles
A right triangle has legs of length 5 and 12 . What is the length of the hypotenuse ?
💡 Memory Point
a² + b² = c² where c = hypotenuse (always the longest side, opposite the right angle).
Common triples to memorize: 3-4-5 | 5-12-13 | 8-15-17
A 10B 11C 13D 17
📖 Step-by-Step Solution
a² + b² = c²
5² + 12² = c²
25 + 144 = 169
c = √169 =
13
This is the famous 5-12-13 Pythagorean triple!
G04
CIRCLE · AREA vs CIRCUMFERENCE
Circles
A circle has a diameter of 10 cm . Which is greater — its circumference or its area? And what is the area ? (Use π ≈ 3.14)
💡 Memory Point
r = diameter ÷ 2
Circumference = 2πr | Area = πr²
Trap: don't use diameter in the formula — always convert to radius first!
A Area = 31.4 cm²B Area = 78.5 cm²; circumference = 31.4 cm — circumference is biggerC Area = 314 cm²D Area = 78.5 cm²; circumference = 31.4 cm — area is bigger
📖 Step-by-Step Solution
Diameter = 10 → radius r = 5 cm
Area = πr² = 3.14 × 25 =
78.5 cm²
Circumference = 2πr = 2 × 3.14 × 5 = 31.4 cm
78.5 > 31.4, so the area is numerically greater. (Note: they have different units — cm² vs cm — but the numerical value of area is larger.)
G05
PARALLEL LINES · ANGLES
Parallel Lines & Transversals
Two parallel lines are cut by a transversal. One angle measures 110° . What is the measure of the co-interior (same-side interior) angle ?
💡 Memory Point
Angle pair rules with parallel lines:
Alternate interior = equal | Corresponding = equal | Co-interior (same-side) =
supplementary (sum = 180°)
A 70°B 110°C 55°D 80°
📖 Step-by-Step Solution
Co-interior angles are supplementary: they add up to 180°.
180° − 110° =
70°
Trap: students often say 110° (thinking they're equal). Equal angles = alternate interior or corresponding. Same-side interior = supplementary!
G06
VOLUME · RECTANGULAR PRISM
3D Shapes
A box has length 8 cm , width 5 cm , and height 3 cm . What is its surface area ?
💡 Memory Point
SA = 2(lw + lh + wh) — there are 3 pairs of identical faces.
Think: top+bottom, front+back, left+right. Each pair counted twice.
A 79 cm²B 158 cm²C 120 cm²D 240 cm²
📖 Step-by-Step Solution
SA = 2(lw + lh + wh)
= 2(8×5 + 8×3 + 5×3)
= 2(40 + 24 + 15)
= 2(79)
=
158 cm²
G07
SIMILAR TRIANGLES · SCALE
Similar Figures
Two similar triangles have corresponding sides in ratio 2 : 5 . If the area of the smaller triangle is 12 cm² , what is the area of the larger triangle?
💡 Memory Point
AREA RATIO = (side ratio)²
If sides ratio = 2:5, area ratio = 2²:5² = 4:25
Don't just multiply the area by the side ratio — square it!
A 30 cm²B 48 cm²C 75 cm²D 60 cm²
📖 Step-by-Step Solution
Side ratio = 2:5 → Area ratio = 4:25
4/25 = 12/x
4x = 300
x =
75 cm²
Trap: 12 × (5/2) = 30 → WRONG! You must use the squared ratio.
G08
EXTERIOR ANGLE THEOREM
Triangles
In a triangle, two interior angles measure 40° and 75° . What is the measure of the exterior angle adjacent to the third interior angle?
💡 Memory Point
EXTERIOR ANGLE = sum of the two non-adjacent interior angles
No need to find the interior angle first — just add the two remote interior angles!
A 65°B 115°C 105°D 180°
📖 Step-by-Step Solution
Exterior angle = sum of two non-adjacent interior angles
= 40° + 75° =
115°
Verify: Third interior angle = 180−40−75 = 65°. Exterior = 180−65 = 115° ✓
G09
COORDINATE GEOMETRY · MIDPOINT
Coordinate Geometry
Points A(2, −3) and B(8, 7) are endpoints of a segment. What is the midpoint and the length of AB?
💡 Memory Point
Midpoint = ( (x₁+x₂)/2 , (y₁+y₂)/2 )
Distance = √[(x₂−x₁)² + (y₂−y₁)²]
Midpoint: average the x's, average the y's.
A Midpoint (5, 2); Length = 2√34B Midpoint (5, 2); Length = √136C Midpoint (3, 2); Length = 12D Midpoint (5, 4); Length = 10
📖 Step-by-Step Solution
Midpoint = ((2+8)/2, (−3+7)/2) = (5, 2)
Distance = √[(8−2)² + (7−(−3))²] = √[36 + 100] = √136 = 2√34
Note: √136 = √(4×34) = 2√34. Both A and B give the same numerical answer (2√34 = √136), but A expresses it in simplified radical form. Answer:
Midpoint (5,2); Length = 2√34
G10
VOLUME · CYLINDER
3D Shapes
A cylinder has a radius of 6 cm and a height of 10 cm . What is its volume ? (Use π ≈ 3.14)
💡 Memory Point
V = πr²h — it's just the circle area times the height.
Think: stack many circles (each area = πr²) up to height h.
A 376.8 cm³B 1130.4 cm³C 2260.8 cm³D 565.2 cm³
📖 Step-by-Step Solution
V = πr²h = 3.14 × 6² × 10
= 3.14 × 36 × 10
= 3.14 × 360
=
1130.4 cm³
Trap: using diameter (12) instead of radius (6). Always halve the diameter!