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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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