NBT Toets 3

Bepaal die waarde van \(2^{1001} - 2^{1000} -2(2^{999}) \) Determine the value of \(2^{1001} - 2^{1000} -2(2^{999}) \)

Bepaal die waarde van n waarvoor/ Determine the value for which \(4(9^n)-9^n=3^{801}\)

Vir watter waarde(s) van \(c\) sal \(y=3x+c\) 'n raaklyn aan \(y=x^2 -x-3\) wees? For which vaue(s) of \(c\) will \(y=3x+c\) be a tangent to \(y=x^2 -x-3\) ?

Vir watter waarde(s) van \(x\) sal \(\frac{x^2+1}{(x-5)(x+8)}=0\) For which values of \(x\) will \(\frac{x^2+1}{(x-5)(x+8)}=0\)

Vereenvoudig/ Simplify: \(3^{n+4001}+3^{n+4001}+3^{n+4001}=\)

Een van die oplossings van \(y-x+5=0\) en \(y+x^2=1\) is One of the solutions of \(y-x+5=0\) and\(y+x^2=1\) is

Bepaal die volgende term van die ry 4; 6; 12; 30; 84..... Determine the following term in the sequence 4; 6; 12; 30; 84.....

Pinochio se neus is 3 cm lank. Elke keer wat hy 'n leuen vertel, word dit met \(\frac{2}{3}\) van die vorige lengte langer.Bepaal wat die langste is wat sy neus ooit kan word in cm. Pinochio's nose is 3 cm long. Every time he tells a lie, it becomes longer with \(\frac{2}{3}\) of the previous length . Determine what is the longest that his nose can ever be in cm.

Bepaal die aard van die wortels van/ Determine the nature of the roots of \(x^2-2x+7=0\)

Watter formule kan gebruik word om te bepaal hoeveel geld per jaar belê moet word teen 12% p.j. maandeliks saamgestel as daar na 4 jaar R9000 beskikbaar moet wees. Which formula can be used to determine how much money should be invested per year at 12% pa. compounded monthly if R9000 must be available after 4 years.

Beskou die volgende ogief. Dit toon die uurlikse inkomste in rand van 'n groep studente. Watter bedrag wat getoon word is die beste skatting van die interkwartiel variasiewydte: Consider the following ogive. It shows the hourly income in rand of a group of students. Which amount shown is the best estimate of the interquartile range:

Die skets van \(y=ax^2+bx+c\) word getoon. Dan sal die volgende waar wees: The sketch shows \(y=ax^2+bx+c\). Then the following will be true:

Vereenvoudig/ Simplify: \(\frac{3^{2x}-2.9^x}{18^x}\)

Die som van die vierkante van vier opeenvolgende positiewe heelgetalle is 126. Bepaal die som wan die vier getalle. The sum of the squares of four consecutive positive integers is 126. Determine the sum of the four numbers.

Die vierkant (kwadraat) van/ The square of \(5-\sqrt{y^2-25}\) is

Die oplossing van/ The solution of \(-2x^2+x+6\ge 0\) is

Verrenvoudig/ Simplify: \( \frac{sin23^\circ cos67^\circ-1}{tan247^\circ}\)

Die lyne in die skets het vergelykings soos aangedui. Bepaal \(\theta\) The lines in the sketch have equations as shown. Determine \(\theta\)

Die skets toon \(\Delta ABC\) met AB = AC = \(a\). Watter stelling ins onwaar? Oppervlakte = The sketch shows \(\Delta ABC\) with AB = AC = \(a\). Which statement is untruer? Area=

'n Visserman skyf die aantal visse waat hy per dag vang neer. Die volgende balk-grafiek toon die resulate. Die gemiddeld en mediaan van die aantal visse gevang is: A fisherman records the number of fish he catches per day. The following bar graph shows the results. The average and median number of fish caught are: