Pure 3: connecting algebra, calculus and vectors: check 1
Difficulty: ★★☆Info
Maths4U Original · Short practice
Consider \(\displaystyle \frac{1}{\left(5 x + 1\right)^{2}}\) expanded in ascending powers of x.
Write \(\displaystyle a=5\) and \(\displaystyle r=\)\(-2\).
Find the coefficient of x.
Enter one number or fraction. Keep exact values during your working; use at least six decimal places for an approximate final answer. A calculator may be used.
Pure 3: connecting algebra, calculus and vectors: review variant 1
Difficulty: ★★☆Info
Maths4U Original · Short practice
Consider \(\displaystyle \left(6 x + 1\right)^{\frac{3}{2}}\) expanded in ascending powers of x.
Write \(\displaystyle a=6\) and \(\displaystyle r=\)\(\displaystyle \frac{3}{2}\).
Find the coefficient of x.
Enter one number or fraction. Keep exact values during your working; use at least six decimal places for an approximate final answer. A calculator may be used.
Pure 3: connecting algebra, calculus and vectors: check 2
Difficulty: ★★☆Info
Maths4U Original · Short practice
The curve satisfies \(x^2+1xy+y^2=91\). Consider \(\displaystyle P=\)\(\left( 6, \ 5\right)\). For the short checks \(\displaystyle a=1\).
Find the tangent y-intercept there.
Enter one number or fraction. Keep exact values during your working; use at least six decimal places for an approximate final answer. A calculator may be used.
Pure 3: connecting algebra, calculus and vectors: review variant 2
Difficulty: ★★☆Info
Maths4U Original · Short practice
The curve satisfies \(x^2+3xy+y^2=20\). Consider \(\displaystyle P=\)\(\left( 2, \ 2\right)\). For the short checks \(\displaystyle a=3\).
Find the tangent y-intercept there.
Enter one number or fraction. Keep exact values during your working; use at least six decimal places for an approximate final answer. A calculator may be used.
Pure 3: connecting algebra, calculus and vectors: check 3
Difficulty: ★★☆Info
Maths4U Original · Short practice
The integrand is \(f(x)=2 x e^{3 x}\), on real x.
Find f(1).
Enter one number or fraction. Keep exact values during your working; use at least six decimal places for an approximate final answer. A calculator may be used.
Pure 3: connecting algebra, calculus and vectors: review variant 3
Difficulty: ★★☆Info
Maths4U Original · Short practice
The integrand is \(f(x)=3 x^{2} e^{x}\), on real x.
Find f(1).
Enter one number or fraction. Keep exact values during your working; use at least six decimal places for an approximate final answer. A calculator may be used.
Pure 3: connecting algebra, calculus and vectors: check 4
Difficulty: ★★☆Info
Maths4U Original · Short practice
The lines are \(\mathbf r=\left[\begin{matrix}22\\2\\1\end{matrix}\right]+t\left[\begin{matrix}1\\3\\4\end{matrix}\right]\), \(\mathbf r=\left[\begin{matrix}21\\12\\10\end{matrix}\right]+u\left[\begin{matrix}4\\-1\\3\end{matrix}\right]\).
Find the intersection y-coordinate.
Enter one number or fraction. Keep exact values during your working; use at least six decimal places for an approximate final answer. A calculator may be used.
Pure 3: connecting algebra, calculus and vectors: review variant 4
Difficulty: ★★☆Info
Maths4U Original · Short practice
The lines are \(\mathbf r=\left[\begin{matrix}23\\2\\2\end{matrix}\right]+t\left[\begin{matrix}2\\4\\5\end{matrix}\right]\), \(\mathbf r=\left[\begin{matrix}21\\22\\14\end{matrix}\right]+u\left[\begin{matrix}5\\-2\\4\end{matrix}\right]\).
Find the intersection y-coordinate.
Enter one number or fraction. Keep exact values during your working; use at least six decimal places for an approximate final answer. A calculator may be used.