Topics

From one-step equations to quadratics and systems.

1. 1Two-step equationsSolve for x: $2x+5=13$Start
2. 2Variables on both sidesSolve for x: $3(x-2)=2x+4$Open
3. 3Equations with fractionsSolve for x: $\frac{x}{3}+\frac{x}{4}=7$Open
4. 4Solving quadratics by factoringSolve by factoring: $x^2-5x+6=0$Open
5. 5The quadratic formulaSolve with the quadratic formula: $2x^2+3x-2=0$Open
6. 6Systems of two equationsSolve the system: $2x+y=7,x-y=2$Open

Angles, Pythagoras, area, similar triangles and distance.

1. 1Angles in a triangleTwo angles of a triangle are 47° and 68°. Find the third angle. $47^{\circ }+68^{\circ }+x=180^{\circ }$Start
2. 2The Pythagorean theoremA right triangle has legs 6 and 8. Find the hypotenuse c. $6^2+8^2=c^2$Open
3. 3Area of a trapezoidFind the area of a trapezoid with parallel sides 6 and 10 and height 4: $A=\frac{1}{2}(a+b)h$Open
4. 4Area and circumference of a circleFind the area and circumference of a circle with radius 5: $r=5$Open
5. 5Similar trianglesA 2 m post casts a 3 m shadow. At the same time a tree casts a 12 m shadow. How tall is the tree? $\frac{h}{12}=\frac{2}{3}$Open
6. 6Distance between two pointsFind the distance between the points: $(1,2)\text{ and }(7,10)$Open

Right-triangle ratios, the unit circle, equations and the law of cosines.

1. 1Sine, cosine and tangentIn a right triangle the side opposite θ is 5 and the hypotenuse is 13. Find cos θ and tan θ. $\sin \theta =\frac{5}{13}$Start
2. 2Finding a missing sideA right triangle has hypotenuse 10 and an angle of 30°. Find the side x opposite that angle. $\sin 30^{\circ }=\frac{x}{10}$Open
3. 3The unit circleFind the exact value: $\cos \frac{2\pi }{3}$Open
4. 4Pythagorean identitiesSimplify: ${\sin }^{2}x+{\sin }^{2}x{\cot }^{2}x$Open
5. 5Solving trig equationsSolve for 0 ≤ x < 2π: $2\sin x-1=0$Open
6. 6The law of cosinesA triangle has sides 5 and 8 with a 60° angle between them. Find the third side c. $c^2=5^2+8^2-2(5)(8)\cos 60^{\circ }$Open

The power, product and chain rules, implicit differentiation and tangent lines.

1. 1The power ruleFind the derivative: $3x^4-5x^2+7$Start
2. 2The product ruleFind the derivative: $x^2\sin x$Open
3. 3The chain ruleFind the derivative: $(3x^2+1{)}^5$Open
4. 4Implicit differentiationFind dy/dx: $x^2+y^2=25$Open
5. 5Tangent linesFind the tangent line at x = 1: $y=x^3-2x$Open

Vectors, matrix products, determinants, inverses and eigenvalues.

1. 1Adding and scaling vectorsCompute: $2\left(\begin{array}{c}1\\ 3\end{array}\right)+\left(\begin{array}{c}4\\ -1\end{array}\right)$Start
2. 2The dot productFind the dot product: $\left(\begin{array}{c}2\\ -1\\ 3\end{array}\right)\cdot \left(\begin{array}{c}4\\ 0\\ -2\end{array}\right)$Open
3. 3Multiplying matricesMultiply the matrices: $\left(\begin{array}{cc}1& 2\\ 3& 4\end{array}\right)\left(\begin{array}{cc}2& 0\\ 1& 3\end{array}\right)$Open
4. 4The determinantFind the determinant: $\left|\begin{array}{cc}3& 1\\ 2& 4\end{array}\right|$Open
5. 5The inverse of a 2×2 matrixFind the inverse: $\left(\begin{array}{cc}4& 7\\ 2& 6\end{array}\right)$Open
6. 6EigenvaluesFind the eigenvalues: $\left(\begin{array}{cc}2& 1\\ 1& 2\end{array}\right)$Open

Speed, acceleration, falling, Newton's second law, ramps and projectiles.

1. 1Average speedA car travels 150 km in 2.5 hours. Find its average speed. $v=\frac{d}{t}$Start
2. 2Constant accelerationA car starts from rest and speeds up at 3 m/s² for 4 s. Find its final speed and how far it goes. $v=v_0+at,x=v_{0}t+\frac{1}{2}a{t}^2$Open
3. 3Free fallA ball is dropped from a height of 44.1 m. How long does it take to reach the ground? Use g = 9.8 m/s². $h=\frac{1}{2}g{t}^2$Open
4. 4Newton's second lawA 5 kg box is pushed with a 30 N force while friction pulls back with 10 N. Find its acceleration. $F_{\text{net}}=ma$Open
5. 5Forces on a rampA block slides down a frictionless ramp tilted at 30°. Find its acceleration. Use g = 9.8 m/s². $a=g\sin \theta$Open
6. 6ProjectilesA ball is thrown horizontally at 15 m/s off a 19.6 m tall cliff. How far from the base does it land? Use g = 9.8 m/s². $y=\frac{1}{2}g{t}^2,x=v_{x}t$Open