ACT Preparation / Unit 23 ACT 2216 review, 2 to 3 minutes
A Mixed Math Set
The idea
Mathematics questions are self-contained and ask for the correct answer. Basic formulas and computation are assumed, but complex formulas and long computation are not required, and a permitted calculator is allowed. Pace a little over a minute a question, faster on easy items, and flag what stalls.
In practice
Worked set, six invented questions. One: if 3(x − 4) = 2x + 1, what is x? 3x − 12 = 2x + 1, so x = 13. Two: a line passes through (1, 2) and (3, 8); what is its slope? (8 − 2)/(3 − 1) = 3. Three: what are the solutions of x² − x − 6 = 0? (x − 3)(x + 2) = 0, so 3 and −2. Four: a right triangle has legs 9 and 12; what is the hypotenuse? 9, 12, 15 is 3, 4, 5 times 3, so 15. Five: a bag holds 4 red and 6 blue marbles, and two are drawn without replacement; what is the probability both are red? 4/10 × 3/9 = 12/90 = 2/15. Six: 15% of what number is 12? 12 ÷ 0.15 = 80. Each took one move after the right recognition: distributing, the slope formula, factoring, a triple, a second draw from a smaller bag, and the percent equation solved for the whole.
Where people slip
Recognition is the skill these six share: each question names its tool if you read it closely. Without replacement changes the second probability; a triple saves a square root; factoring beats the formula when the numbers are small. Where a question gives a part and its percent, divide to find the whole, as question six does. Check each answer against the question before moving on.
Your place on the trail
Every lesson rests on earlier ones and opens later ones. Tap any to jump.
Builds on
Unlocks
- Nothing yet depends on this.
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