MYP Mathematics 9–10 | Core Concepts Mastery Quiz

IB MYP Curriculum Aligned

Are you ready to test your skills?

20 multiple-choice questions across all MYP Math units. Study the concept cards first, then attempt the quiz. Answers with full worked solutions appear at the end.

Before You Begin

📚 Concept Review — All Units

Unit 1

Algebra & Equations

Algebra is the language of mathematics, using symbols to represent quantities and relationships.

Key Formulas

Quadratic Formula: $x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

Difference of Squares: $a^2 - b^2 = (a+b)(a-b)$

Perfect Square: $(a \pm b)^2 = a^2 \pm 2ab + b^2$

Discriminant$\Delta = b^2 - 4ac$: $>0$ two roots, $=0$ one root, $<0$ no real roots

Sum of roots$\alpha + \beta = -b/a$

Product of roots$\alpha \cdot \beta = c/a$

Worked Example

Solve $2x^2 - 5x - 3 = 0$

$x = \dfrac{5 \pm \sqrt{25+24}}{4} = \dfrac{5 \pm 7}{4}$ → $x = 3$ or $x = -\tfrac{1}{2}$

Unit 2

Linear & Quadratic Functions

Functions describe relationships between variables. The graph of a function reveals its behavior visually.

Key Formulas

Slope: $m = \dfrac{y_2 - y_1}{x_2 - x_1}$ Line: $y = mx + c$

Vertex form: $y = a(x-h)^2 + k$ vertex at $(h, k)$

Standard to vertex: complete the square

Worked Example

Find vertex of $y = x^2 - 4x + 7$

$y = (x-2)^2 + 3$ → Vertex: $(2, 3)$

Unit 3

Geometry — Area, Volume & Similarity

Key Formulas

Circle: Area $= \pi r^2$, Circumference $= 2\pi r$

Cylinder: $V = \pi r^2 h$ Cone: $V = \tfrac{1}{3}\pi r^2 h$

Sphere: $V = \tfrac{4}{3}\pi r^3$ Surface area $= 4\pi r^2$

Similar figures: $\dfrac{\text{Area}_1}{\text{Area}_2} = \left(\dfrac{l_1}{l_2}\right)^2$

Pythagoras$a^2 + b^2 = c^2$ (right triangle)

Similar ratioLength $k$, Area $k^2$, Volume $k^3$

Unit 4

Trigonometry

SOH CAH TOA + Laws

$\sin\theta = \dfrac{\text{opp}}{\text{hyp}}$ $\cos\theta = \dfrac{\text{adj}}{\text{hyp}}$ $\tan\theta = \dfrac{\text{opp}}{\text{adj}}$

Sine Rule: $\dfrac{a}{\sin A} = \dfrac{b}{\sin B} = \dfrac{c}{\sin C}$

Cosine Rule: $c^2 = a^2 + b^2 - 2ab\cos C$

Area of triangle: $A = \tfrac{1}{2}ab\sin C$

Worked Example

In △ABC: $a=7$, $b=5$, $C=60°$. Find $c$.

$c^2 = 49+25-2(7)(5)\cos60° = 74-35 = 39$ → $c = \sqrt{39} \approx 6.24$

Unit 5

Statistics & Probability

Key Formulas

Mean: $\bar{x} = \dfrac{\sum x}{n}$    Median: middle value

$P(A \cup B) = P(A) + P(B) - P(A \cap B)$

$P(A|B) = \dfrac{P(A \cap B)}{P(B)}$   (Conditional probability)

IQR $= Q_3 - Q_1$   Outlier: $< Q_1 - 1.5\times\text{IQR}$ or $> Q_3 + 1.5\times\text{IQR}$

Unit 6

Sequences & Series

Arithmetic Sequences

$u_n = u_1 + (n-1)d$ $S_n = \dfrac{n}{2}(u_1 + u_n) = \dfrac{n}{2}(2u_1 + (n-1)d)$

Geometric Sequences

$u_n = u_1 \cdot r^{n-1}$ $S_n = \dfrac{u_1(r^n - 1)}{r-1}$ $(r \neq 1)$

Unit 7

Indices (Exponents) & Logarithms

Index Laws

$a^m \cdot a^n = a^{m+n}$ $\dfrac{a^m}{a^n} = a^{m-n}$ $(a^m)^n = a^{mn}$

$a^0 = 1$ $a^{-n} = \dfrac{1}{a^n}$ $a^{1/n} = \sqrt[n]{a}$

Logarithm Laws

$\log(ab) = \log a + \log b$ $\log\dfrac{a}{b} = \log a - \log b$ $\log a^n = n\log a$

Exam Practice

📝 20 Questions — Answer All

Q01 Algebra — Discriminant Easy

How many real solutions does $3x^2 - 4x + 2 = 0$ have?

Q02 Algebra — Quadratic Formula Medium

The solutions to $x^2 - 5x + 6 = 0$ are:

Q03 Functions — Vertex of Parabola Medium

What is the vertex of the parabola $y = x^2 - 6x + 11$?

Q04 Functions — Gradient Easy

A line passes through $(1, 3)$ and $(4, 9)$. What is its gradient?

Q05 Geometry — Circle Area Easy

A circle has diameter $10$ cm. What is its area? (Leave in terms of $\pi$.)

Q06 Geometry — Volume of Cone Medium

A cone has radius $6$ cm and height $10$ cm. What is its volume? (Give answer in terms of $\pi$.)

Q07 Trigonometry — Sine Rule Medium

In triangle $ABC$, $\angle A = 30°$, $\angle B = 45°$, and $a = 8$ cm. Using the sine rule, find side $b$ (to 2 decimal places).

Q08 Sequences — Arithmetic Easy

The first term of an arithmetic sequence is $5$ and the common difference is $3$. What is the 20th term?

Q09 Sequences — Geometric Medium

The first term of a geometric sequence is $2$ and the common ratio is $3$. What is the sum of the first 5 terms?

Q10 Indices — Laws of Exponents Easy

Simplify: $\dfrac{x^5 \cdot x^{-2}}{x^3}$

Q11 Probability — Union Medium

$P(A) = 0.4$, $P(B) = 0.5$, $P(A \cap B) = 0.2$. Find $P(A \cup B)$.

Q12 Geometry — Similar Figures Medium

Two similar triangles have corresponding sides in ratio $3:5$. If the area of the smaller triangle is $27$ cm², what is the area of the larger triangle?

Q13 Indices — Logarithm Medium

Solve for $x$: $\log_2(x) + \log_2(4) = 5$

Q14 Statistics — Mean Medium

The values $4, 7, 7, 9, 13$ have a mean of:

Q15 Trigonometry — Triangle Area Medium

Two sides of a triangle are $8$ cm and $10$ cm, and the included angle is $30°$. Find the area of the triangle.

Q16 Algebra — Factorisation Hard

Factorise completely: $6x^2 + 7x - 3$

Q17 Probability — Conditional Hard

A bag contains $3$ red and $5$ blue balls. Two balls are drawn without replacement. What is the probability that both are red?

Q18 Sequences — Arithmetic Sum Hard

Find the sum of all integers from $1$ to $100$ inclusive.

Q19 Indices — Fractional Exponents Hard

Evaluate: $\left(\dfrac{27}{8}\right)^{2/3}$

Q20 Trigonometry — Cosine Rule Hard

In triangle $PQR$, $PQ = 7$, $QR = 9$, and $\angle Q = 120°$. Find $PR$ (to 2 d.p.).

Quiz Complete

out of 20

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Percentage—

Time Used—

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📋 Answer Key & Full Solutions

Q01ADiscriminant

Identify coefficients: $a=3$, $b=-4$, $c=2$.

Calculate discriminant: $\Delta = (-4)^2 - 4(3)(2) = 16 - 24 = -8$.

Since $\Delta < 0$, there are no real solutions. ✓ Answer: A

Q02CQuadratic Formula

Factor: find two numbers that multiply to $+6$ and add to $-5$: those are $-2$ and $-3$.

$(x-2)(x-3) = 0$ → $x = 2$ or $x = 3$. ✓ Answer: C

Check: $(2)^2 - 5(2)+6 = 4-10+6=0$ ✓ and $(3)^2-5(3)+6=9-15+6=0$ ✓

Q03BVertex of Parabola

Complete the square: $y = x^2 - 6x + 11$.

$y = (x^2 - 6x + 9) + 11 - 9 = (x-3)^2 + 2$.

Vertex is $(h, k) = (3, 2)$. ✓ Answer: B

Q04CGradient

$m = \dfrac{y_2 - y_1}{x_2 - x_1} = \dfrac{9-3}{4-1} = \dfrac{6}{3} = 2$. ✓ Answer: C

Q05BCircle Area

Diameter $= 10$ cm, so radius $r = 5$ cm.

Area $= \pi r^2 = \pi(5)^2 = 25\pi$ cm². ✓ Answer: B

Q06CVolume of Cone

$V = \tfrac{1}{3}\pi r^2 h = \tfrac{1}{3}\pi(6)^2(10) = \tfrac{1}{3}\pi(360) = 120\pi$ cm³. ✓ Answer: C

Q07CSine Rule

Sine rule: $\dfrac{b}{\sin B} = \dfrac{a}{\sin A}$

$\dfrac{b}{\sin 45°} = \dfrac{8}{\sin 30°}$

$b = \dfrac{8 \times \sin 45°}{\sin 30°} = \dfrac{8 \times \frac{\sqrt{2}}{2}}{\frac{1}{2}} = 8\sqrt{2} \approx 11.31$ cm. ✓ Answer: C

Q08BArithmetic Sequence

$u_n = u_1 + (n-1)d = 5 + (20-1)(3) = 5 + 57 = 62$. ✓ Answer: B

Q09BGeometric Series Sum

$S_5 = \dfrac{u_1(r^5 - 1)}{r-1} = \dfrac{2(3^5-1)}{3-1} = \dfrac{2(243-1)}{2} = 242$. ✓ Answer: B

Check: $2+6+18+54+162 = 242$ ✓

Q10AIndex Laws

Numerator: $x^5 \cdot x^{-2} = x^{5+(-2)} = x^3$.

$\dfrac{x^3}{x^3} = x^{3-3} = x^0 = 1$. ✓ Answer: A

Q11DProbability Union

$P(A \cup B) = P(A) + P(B) - P(A \cap B) = 0.4 + 0.5 - 0.2 = 0.7$. ✓ Answer: D

Q12CSimilar Figures

Length ratio $= 3:5$, so area ratio $= 3^2 : 5^2 = 9 : 25$.

$\dfrac{27}{\text{Area}_2} = \dfrac{9}{25}$ → Area$_2 = \dfrac{27 \times 25}{9} = 75$ cm². ✓ Answer: C

Q13BLogarithms

$\log_2(x) + \log_2(4) = 5$ → $\log_2(4x) = 5$.

$4x = 2^5 = 32$ → $x = 8$. ✓ Answer: B

Check: $\log_2(8) + \log_2(4) = 3 + 2 = 5$ ✓

Q14CMean

Sum $= 4+7+7+9+13 = 40$. Count $= 5$.

Mean $= 40 \div 5 = 8$. ✓ Answer: C

Q15ATriangle Area

$A = \tfrac{1}{2}ab\sin C = \tfrac{1}{2}(8)(10)\sin 30°$.

$= \tfrac{1}{2}(80)(0.5) = 20$ cm². ✓ Answer: A

Q16DFactorisation

Multiply $6 \times (-3) = -18$. Find two numbers that multiply to $-18$ and add to $+7$: these are $+9$ and $-2$.

$6x^2 + 9x - 2x - 3 = 3x(2x+3) - 1(2x+3) = (3x-1)(2x+3)$.

Check: $(3x-1)(2x+3) = 6x^2+9x-2x-3 = 6x^2+7x-3$ ✓ Answer: D

Q17BConditional Probability

Total balls $= 8$. $P(\text{1st red}) = \dfrac{3}{8}$.

Without replacement: $P(\text{2nd red} | \text{1st red}) = \dfrac{2}{7}$.

$P(\text{both red}) = \dfrac{3}{8} \times \dfrac{2}{7} = \dfrac{6}{56} = \dfrac{3}{28}$. ✓ Answer: B

Q18CArithmetic Sum

$S_{100} = \dfrac{n}{2}(u_1 + u_n) = \dfrac{100}{2}(1+100) = 50 \times 101 = 5050$. ✓ Answer: 5050

Q19BFractional Exponents

$\left(\dfrac{27}{8}\right)^{2/3} = \left(\dfrac{27}{8}\right)^{1/3 \times 2}$.

Cube root first: $\left(\dfrac{27}{8}\right)^{1/3} = \dfrac{\sqrt[3]{27}}{\sqrt[3]{8}} = \dfrac{3}{2}$.

Square the result: $\left(\dfrac{3}{2}\right)^2 = \dfrac{9}{4}$. ✓ Answer: B

Q20CCosine Rule

Cosine rule: $PR^2 = PQ^2 + QR^2 - 2(PQ)(QR)\cos Q$.

$PR^2 = 7^2 + 9^2 - 2(7)(9)\cos 120°$.

$\cos 120° = -\tfrac{1}{2}$, so $PR^2 = 49 + 81 - 2(7)(9)(-\tfrac{1}{2}) = 130 + 63 = 193$.

$PR = \sqrt{193} \approx 13.89$. ✓ Answer: C