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United StatesMaths

Number and Quantity

5 dot points across 5 inquiry questions. Click any dot point for a focused answer with worked past exam questions where available.

How do you apply the laws of exponents, simplify roots, and work with scientific notation on the ACT?

Apply integer and rational exponent laws, simplify and operate with square and higher roots, and convert and compute with numbers in scientific notation (Number and Quantity).
An ACT Number and Quantity answer on the laws of exponents (including negative and rational exponents), simplifying square and higher roots, rationalising, and converting and calculating with scientific notation, with worked ACT-style questions.
11 min answer →

How do you compute percentages, percent change, and reverse percentages on the ACT?

Compute a percentage of a number, percent increase and decrease, successive and reverse percentages, and simple interest in real contexts (Number and Quantity, Integrating Essential Skills).
An ACT answer on percentages: finding a percent of a number, percent increase and decrease, successive percentages, reverse percentages to recover an original amount, and simple interest, with worked ACT-style questions.
10 min answer →

How do you set up and solve ratio, proportion and rate problems on the ACT?

Set up and solve ratios, proportions and rates, including unit rates, scaling, direct and inverse variation, and unit conversion (Number and Quantity, Integrating Essential Skills).
An ACT answer on ratios, proportions and rates: setting up a proportion, sharing in a ratio, unit rates and unit conversion, and direct and inverse variation, with worked ACT-style questions and common traps.
10 min answer →

How do you classify real numbers and perform basic operations with complex numbers on the ACT?

Classify numbers within the real number system, work with absolute value, and add, subtract, multiply and simplify complex numbers using $i^{2} = -1$ (Number and Quantity).
An ACT Number and Quantity answer on classifying real numbers (integers, rationals, irrationals), absolute value, and operating with complex numbers using i squared equals negative one, including multiplying and simplifying expressions with i.
10 min answer →

How do you perform basic vector and matrix operations on the ACT?

Add, subtract and scalar-multiply vectors and matrices, find a vector's magnitude, and multiply small matrices (Number and Quantity).
An ACT Number and Quantity answer on vectors and matrices: adding, subtracting and scaling vectors, finding magnitude, and adding, scaling and multiplying small matrices, with worked ACT-style questions and common traps.
10 min answer →