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The NBT Mathematics (MAT) test: Exemplar questions Questions in the section Functions and their Graphs will determine whether a test writer understands the properties of parabolas. Questions 1 and 2 are examples. 1. The function f defined by y = f ( x) = − x 2 + 6 x − 5 has (A) A minimum ?? value and a negative ??-intercept. (B) A maximum ?? value and a positive ??-intercept. (C) A minimum
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The NBT Mathematics (MAT) test: Exemplar questions Questions in the section Functions and their Graphs  will determine whether a test writer understands the properties of parabolas. Questions 1 and 2 are examples. 1.   The function  f    defined by 56)(  2 −+−==  x x x f  y has (A)   A minimum   value and a negative  -intercept. (B)   A maximum   value and a positive  -intercept. (C)   A minimum   value and a positive  -intercept. (D)   A maximum   value and a negative  -intercept. Under the heading Algebraic Processes one of the topics listed is  Algebraic Manipulation . Question 2 is an example of a question where the answer cannot be deduced by substituting into the given options to rule out those that are correct. 2. The sum of the roots of the equation − 2 +6  − 5=0  is (A)   − 5  (B) − 4  (C) 3  (D) 6  Another topic listed under the heading Algebraic Processes is Number Sense. The following question depends on Number Sense (the bigger a number, the bigger its square root) as well as the concepts tested in the first two questions above. 3. The expression √ − 2 +6  − 5  has a (A) maximum value of 2  (B) minimum value of 2  (C) maximum value of 3  (D) minimum value of 3  Question 4 is an example of the category Transformations  and related concepts. 4. If the graph of  =  − 2 +6  − 5  is reflected in the  -axis and the resulting graph is then reflected in the  -axis, the new equation is (A)  =  − (  − 3) 2 +4  (B)  =  − 2 − 6  − 5  (C)  =(  +3) 2 +4  (D)  =   2 +6  +5  One of the categories listed is Competent use of logical skills in making deductions and determining the validity of given assertions. Question 5 (which is also an example Number Sense) illustrates what this means. Writers need to assess the various options and make deductions about their validity.  5. For any real number   , which one of the following statements is always  true?   (A)   − <0  (B)  x  1 is rational (C) 11 <+  x  x   (D) 11 >  x   if 0<   <1  The next two questions are in the Trigonometry   category. Question 6 depends on an understanding of compound angles , and question 7 involves an application of trigonometric ratios  in a two-dimensional situation. 6. sin43 ° cos23 ° − cos43 ° sin23 °  is equal to (A)   cos66 °  (B) cos20 °  (C) sin66 °  (D) sin20 °  7. The angle of elevation of the top of cell phone tower B from the top of cell phone tower A is 30 ° . The angle of depression of the foot of cell phone tower B from the top of cell phone tower A is 60 ° . The height of cell phone tower B is 100 m. The foot of cell phone tower A and the foot of cell phone tower B are in the same horizontal plane. The height of cell phone tower A is (A) 60 m (B) 65 m (C) 70 m (D) 75 m Question 8 combines an understanding of  Algebraic Manipulation  (in this case quadratics) and Spatial Awareness  (rectangles) and Question 9 tests understanding of the Properties of two- and three-dimensional objects,  as well as surface area .  8. Suppose ABCD is a square with side length (  − 1)  cm. If the area of rectangle ABFE is (  2 +  − 2)  cm², then the length of FC, in cm, is (A) 2 (B) 3 (C) 4 (D) 5 Question 9 is also an example of Spatial Awareness . 9. The figure represents an empty cube with a circular opening at the top. The diameter of the opening is half the length of the diagonal AB. The outer surface area of the cube (in square centimetres) is: (A) 6  2 −   4  (B) 6  2 − 2  2  (C) 6  2 −   8  (D) 6  2 −   2  Question 10 (from the  Algebraic Processes  subcategory Financial Calculations ) shows what we mean when we say that calculators are unnecessary. 10. An amount of R1 000 is invested at an annual interest rate of 6%. Interest is compounded every three months  (quarterly). After 5 years the investment, in rands, will be worth (A) 1 000 (1,015) 20  (B) 1 000 (1,02) 15  (C) 1 000 (1,03) 20  (D)  1 000 (1,06) 5  The options given above show that we are interested in the expression you would use to carry out the calculation, and not in the final answer.
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