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NAT Grade 10 — Mathematics - NAT GRADE-10 Study Notes

Comprehensive reviewer for the National Achievement Test (NAT) Grade 10 — Mathematics. It covers the most-tested skills with worked examples and test strategy.

Number Sense & Operations

Master the four operations on integers, fractions, and decimals, plus the order of operations.

GEMDAS: Grouping \to Exponents \to Mult/Div \to Add/Sub

Operation	Rule	Example
(−)(−)	positive	(−4)(−2)=8
Add fractions	common denominator first	1/2+1/3=5/6
Percent	part = rate × base	20% of 50 = 10

⚠️ Common Mistake

Do operations inside parentheses and exponents BEFORE multiplying or adding. Left-to-right for same-level operations.

Algebra

Translate words into equations and solve linear and quadratic equations.

Linear: 2x + 3 = 11 \to x = 4 Quadratic: x = [-b \pm \sqrt(b²-4ac)] \div 2a

💡 Exam Hack

Keywords: "is" = (=), "of" = (×), "more than" = (+), "less than" = (−). Build the equation, then isolate the variable.

Geometry & Measurement

Figure	Perimeter	Area
Rectangle	2(L+W)	L×W
Triangle	a+b+c	½bh
Circle	C=πd	πr²

Right triangle: a² + b² = c² Volume of box = L\timesW\timesH

⚠️ Common Mistake

Perimeter is the distance AROUND (1D, units like cm); area is the space INSIDE (2D, units like cm²). Do not mix them.

Statistics & Probability

Measure	How to find
Mean	sum ÷ count
Median	middle of ordered data
Mode	most frequent

P(event) = favorable \div total outcomes Permutation nPr (order matters); Combination nCr (order not)

💡 Exam Hack

Always ARRANGE data before finding the median. Probability is always between 0 and 1.

Sequences & Patterns

Sequence	Rule	nth term
Arithmetic	add d	aₙ=a₁+(n−1)d
Geometric	multiply r	aₙ=a₁·r^(n−1)

Identify the pattern first: are you ADDING a constant (arithmetic) or MULTIPLYING (geometric)?

Trigonometry

SOH-CAH-TOA \cdot sin=Opp/Hyp \cdot cos=Adj/Hyp \cdot tan=Opp/Adj

💡 Exam Hack

Label the sides relative to the angle (opposite, adjacent, hypotenuse), then pick the ratio using the two sides involved.

Worked Examples

1. A shirt costs ₱500 with a 20% discount. Final price?

Discount = 500 \times 0.20 = 100 \to Price = 500 - 100 = ₱400

2. Find the mean of 12, 15, 18, 15.

(12+15+18+15) \div 4 = 60 \div 4 = 15

3. Solve x² − 7x + 12 = 0.

(x-3)(x-4)=0 \to x = 3 or 4

Test-Taking Strategy

💡 Exam Hack

Read carefully and underline what is ASKED. Eliminate impossible options. Substitute answer choices back when stuck. Do easy items first; never leave blanks — there is no wrong-answer penalty.

⚠️ Common Mistake

Watch units and "EXCEPT/NOT" questions. Re-check whether the question wants the value, the difference, or the percentage.