WISKUNDE
GRAAD 10
NOG OEFENINGE
Lineêre funksies en hulle grafieke.
GRAAD 10
NOG OEFENINGE
Lineêre funksies en hulle grafieke.
MATHEMATICS
GRADE 10
MORE EXERCISES
Linear functions and their graphs.
GRADE 10
MORE EXERCISES
Linear functions and their graphs.
Bereken die afsnitte op die asse vir elk van
die volgende funksies en skets dan hulle
grafieke. Toon al die afsnitte duidelik aan :
1.1 y = x + 3
1.3 y = −4x + 3
die volgende funksies en skets dan hulle
grafieke. Toon al die afsnitte duidelik aan :
1.1 y = x + 3
1.3 y = −4x + 3
Calculate the intercepts on he axes for each of
the following functions and then sketch theit graphs.
Show all intercepts clearly :
1.2 y = 2x − 5
1.4 y = −3x − 1
the following functions and then sketch theit graphs.
Show all intercepts clearly :
1.2 y = 2x − 5
1.4 y = −3x − 1
Die volgende figure stel die grafieke voor van
funksies wat gedefinieer word deur f(x) = mx + c.
Bepaal in elke geval die waardes van m en c en
skryf dan die vergelyking in die vorm y = mx + c.
2.1
Antwoord / Answer 2.1
2.3
Antwoord / Answer 2.3
funksies wat gedefinieer word deur f(x) = mx + c.
Bepaal in elke geval die waardes van m en c en
skryf dan die vergelyking in die vorm y = mx + c.
2.1
Antwoord / Answer 2.1
2.3
Antwoord / Answer 2.3
The following figures represent the graphs of
functions defined by f(x) = mx + c. In each case
determine the values of m and c and then write
down the equation in the form y = mx + c.
2.2
Antwoord / Answer 2.2
2.4
Antwoord / Answer 2.4
functions defined by f(x) = mx + c. In each case
determine the values of m and c and then write
down the equation in the form y = mx + c.
2.2
Antwoord / Answer 2.2
2.4
Antwoord / Answer 2.4
Die volgende figure stel die grafieke voor van
funksies wat gedefinieer word deur f(x) = mx + c.
en g(x) = px + q. Bepaal in elke geval die waardes
van m, c, p en q en skryf dan die vergelyking
in die vorm y = mx + c.
funksies wat gedefinieer word deur f(x) = mx + c.
en g(x) = px + q. Bepaal in elke geval die waardes
van m, c, p en q en skryf dan die vergelyking
in die vorm y = mx + c.
The following diagrams represent the graphs of
functions defined by f(x) = mx + c and g(x) = px + q.
Determine in each case the values of m, c, p and q
and write down the equation of each function
in the form y = mx + c.
functions defined by f(x) = mx + c and g(x) = px + q.
Determine in each case the values of m, c, p and q
and write down the equation of each function
in the form y = mx + c.
A(0 ; 1); B(2 ; 5); C(0 ; 8) en / and D(3 ; −4)
is punte op f en g. / are points on f and g.
Antwoord / Answer 3.3
Vraag / Question 3.5
3.5
P(−2 ; 3); Q(4 ; 9); R(−1 ; 9) en / and S(3 ; −3)
is punte op die grafieke. / are points on the graphs. 3.5.1 Bereken die koördinate van punte A, B, C
en D. / Calculate the coordinates of
points A, B, C and D.
3.5.2 Bereken die lengte van AD en BC.
/ Calculate the lengths of AD and BC.
Antwoord / Answer 3.5
is punte op f en g. / are points on f and g.
Antwoord / Answer 3.3
Vraag / Question 3.5
3.5
P(−2 ; 3); Q(4 ; 9); R(−1 ; 9) en / and S(3 ; −3)
is punte op die grafieke. / are points on the graphs. 3.5.1 Bereken die koördinate van punte A, B, C
en D. / Calculate the coordinates of
points A, B, C and D.
3.5.2 Bereken die lengte van AD en BC.
/ Calculate the lengths of AD and BC.
Antwoord / Answer 3.5
A(−2 ; 0); B(0 ; 6); P(−1 ; 3) en / and Q(1 ; 1)
is punte op f en g. / are points on f and g. 3.4.1 Bereken die koördinate van C. / Calculate the
coordinates of C.
3.4.2 Bereken die koördinate van D as DP || Y-as /
Calculate the coordinates of D id DP || Y-axis.
3.4.3 Bereken die lengte van DP. / Calculate the length
of DP.
Antwoord / Answer 3.4
Vraag / Question 3.6
3.6
P(−1 ; −11); Q(2 ; −2); R(−3 ; 5) en / and S(2 ; −5)
is punte op f en g. / are points on f and g. 3.6.1 Bereken die koördinate van punte A, B, C
en D. / Calculate the coordinates of
points A, B, C and D.
3.6.2 Bereken die lengte van QS. / Calculate the
length of QS.
3.6.3 Skryf die koördinate van punt V neer as T die
punt (3 ; 1) is en die lengte van TV = 8, /
Write down the coordinates of point V if
T is the point (3 ; 1) and the length of TV = 8.
Antwoord / Answer 3.6
is punte op f en g. / are points on f and g. 3.4.1 Bereken die koördinate van C. / Calculate the
coordinates of C.
3.4.2 Bereken die koördinate van D as DP || Y-as /
Calculate the coordinates of D id DP || Y-axis.
3.4.3 Bereken die lengte van DP. / Calculate the length
of DP.
Antwoord / Answer 3.4
Vraag / Question 3.6
3.6
P(−1 ; −11); Q(2 ; −2); R(−3 ; 5) en / and S(2 ; −5)
is punte op f en g. / are points on f and g. 3.6.1 Bereken die koördinate van punte A, B, C
en D. / Calculate the coordinates of
points A, B, C and D.
3.6.2 Bereken die lengte van QS. / Calculate the
length of QS.
3.6.3 Skryf die koördinate van punt V neer as T die
punt (3 ; 1) is en die lengte van TV = 8, /
Write down the coordinates of point V if
T is the point (3 ; 1) and the length of TV = 8.
Antwoord / Answer 3.6
4.1 A(0 ; 3) en B(2 ; 5) is punte op dieselfde lyn.
Bereken die vergelyking van die lyn.
Antwoord 4.1
4.2 C(0 ; −5) en D(−3 ; −11) is kolineêr (punte op
dieselfde lyn). Berelen die vergelyking van die lyn.
Antwoord 4.2
4.3 M(−2 ; 24) en N(3 ; −6) is punte op dieselfde
lyn). Bereken die vergelyking van die lyn.
Antwoord 4.3
4.4 P(−6 ; 2) en Q(3 ; −7) is kolineêr. Bereken
die vergelyking van die lyn.
Antwoord 4.4
Bereken die vergelyking van die lyn.
Antwoord 4.1
4.2 C(0 ; −5) en D(−3 ; −11) is kolineêr (punte op
dieselfde lyn). Berelen die vergelyking van die lyn.
Antwoord 4.2
4.3 M(−2 ; 24) en N(3 ; −6) is punte op dieselfde
lyn). Bereken die vergelyking van die lyn.
Antwoord 4.3
4.4 P(−6 ; 2) en Q(3 ; −7) is kolineêr. Bereken
die vergelyking van die lyn.
Antwoord 4.4
4.1 A(0 ; 3) and B(2 ; 5) are points on the same line.
Calculate the equation of the line.
Answer 4.1
4.2 C(0 ; −5) and D(−3 ; −11) are colinear (points on
the same line). Calculate the equation of the line.
Answer 4.2
4.3 M(−2 ; 24) and N(3 ; −6) are points on the same
line. Calculate the equation of the line.
Answer 4.3
4.4 P(−6 ; 2) and Q(3 ; −7) are colinear. Calculate
the equation of the line.
Answer 4.4
Calculate the equation of the line.
Answer 4.1
4.2 C(0 ; −5) and D(−3 ; −11) are colinear (points on
the same line). Calculate the equation of the line.
Answer 4.2
4.3 M(−2 ; 24) and N(3 ; −6) are points on the same
line. Calculate the equation of the line.
Answer 4.3
4.4 P(−6 ; 2) and Q(3 ; −7) are colinear. Calculate
the equation of the line.
Answer 4.4
8
8
4.5
Die punte M(— ; 0) en N(−1 ; 13) is
4.5
The points M(— ; 0) and N(−1 ; 13) are
5
5
punte op dieselfde lyn. Bereken die
ponts on the same line. Calculate the
vergelyking van die lyn.
equation of the line.
2
9
8
1
2
9
8
1
4.6
Die punte P(— ; —) en Q(− — ;− —)
4.6
The points P(— ; —) and Q(− — ;− —)
5
2
5
2
5
2
5
2
is punte op dieselfde lyn. Bereken die
are points on the same line. Calculate
vergelyking van die lyn.
the equation of the line.
Vraag / Question 5
Punte P(−5 ; −19) en Q(8 ; 20) is punte op die grafiek van f(x) terwyl punte R(−5 ; 53) en S(4 ; −52) punte op die grafiek van g(x) is.
Points P(−5 ; −19) and Q(8 ; 20) are points on the graph of f(x) while points R(−5 ; 53) and S(4 ; −52) are points on the graph of g(x).
5.1
Bereken die vergelykings van f(x) en g(x).
Calculate the equations of f(x) and g(x).
5.2
Punt A is die Y-afsnit van f(x) en punt B is
5.2
Point A is the Y-intercept of f(x) andpoint
die X-afsnit van f(x). Bereken die
B is the X-interceptt of f(x). Calculate the
koördinate van A en B.
coordinates of A and B.
5.3
Punt C is die Y-afsnit van g(x) en punt D is
5.3
Point C is the Y-intercept of g(x) and point
die X-afsnit van g(x). Bereken die
D is the X-interceptt of g(x). Calculate the
koördinate van C en D.
coordinates of C and D.
5.4
Bereken die koördinate van punt E, die
5.4
Calculate the coordinates of point E, the
snypunt van f(x) en g(x).
point of intersection of f(x) and g(x).
5.5
Bereken die lengte van CA, d(CA)
5.5
Calculate the length of CA, d(CA)
5.6
T is 'n punt op g(x) en V 'n punt op f(x)
5.6
T is a point on g(x) and V a point on f(x)
sodat TV || Y-as.
such that TV || Y-axis.
5.6.1
Bepaal die lengte van TV in terme van x.
5.6.1
Determine the length of TV in terms of x.
5.6.2
Bereken die koördinate van punte T en V
5.6.2
Calculate the coordinates of points T and
as die lengte van TV 60 eenhede is.
V if the length of TV is 60 units.
5.7
Vir watter waarde(s) van x is / For which value(s) of x is
5.7.1
f(x) = 0?
5.7.2
g(x) > 0?
5.7.3
f(x) = g(x)?
5.7.4
f(x) ≥ g(x)?
5.7.5
f(x) × g(x) = 0?
5.7.6
f(x) × g(x) ≥ 0?