5 exercises · 1 automatically checked · 4 written self-checks · Untimed
1 question · Untimed practice
Try each question before choosing Check answer. Guide question labels stay the same when you shuffle the bank. 4 written responses appear below the bank, with model answers for self-review; these are not automatically graded. Follow any rounding instruction in the question.
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Compare the reasoning as well as the answer. Equivalent valid methods are welcome. A referenced example provides a targeted repair route.
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Find the value of −2x2 + 4x when x = −3.
Enter an integer, decimal or fraction without units. Use up to 5 characters, or 6 including a leading minus.
−30.
Substitute with grouped negatives: −2(−3)2 + 4(−3) = −2(9) − 12 = −30. One entry is -2*(-3)^2+4*(-3). The leading −2 is a coefficient, not part of the squared base. A result such as 24 or 6 signals that the sign or grouping changed. Review Example 1.04.
Review Calculator input and settings
Write your complete response before opening the model answer. Compare both your answer and your reasoning.
Evaluate . Write a calculator entry that preserves the intended grouping.
4.
Use (9+7)/(6-2). The numerator is 16 and the denominator is 4, so the quotient is 4. The entry 9+7/6-2 would mean something different because only 7 would be divided by 6. A quick exact calculation checks that the display matches the fraction. Review Example 1.01.
A right triangle has hypotenuse 20. What is the length of the side opposite a 30° angle? Identify the angle setting needed for a numerical sine calculation.
10; degrees.
The side is 20 sin 30° = 20(1/2) = 10. With the calculator in degree mode, use 20*sin(30). The special-triangle relationship provides an independent check: the side opposite 30° is half the hypotenuse. A radian-mode calculation of sin(30) would represent a different angle. Review Example 1.10.
Let f(x) = 3x2 − x + 2. Find f(−2) and give a reusable function-entry method.
16.
Define f(x)=3*x^2-x+2, then evaluate f(-2). Algebra confirms 3(4) − (−2) + 2 = 12 + 2 + 2 = 16. The minus sign before x becomes addition when a negative input is substituted. A function definition is useful when several evaluations are needed, but direct substitution is equally valid for one input. Review Example 1.12.
An old calculator entry defines m = 3. A new problem requires y = mx + 5 with m = −2. What should y be at x = 4, and what must be corrected before relying on the calculator?
−3; replace or remove the old definition.
The new relationship is y