4th Form 2nd half term test

• What is an arithmetic sequence (AS)?

  A sequence with a constant difference
• How is each term in an arithmetic sequence obtained?

  By adding a constant difference
• What is the common difference in the sequence 3, 7, 11, 15, …?

  +4
• What is a geometric sequence (GS)?

  A sequence with a constant ratio
• How is each term in a geometric sequence obtained?

  By multiplying the previous term by a constant ratio
• What is the common ratio in the sequence 2, 6, 18, 54, …?

  ×3
• What is the Fibonacci sequence?

  A sequence where each term is the sum of the two preceding terms
• How do you find the 10th term of the arithmetic sequence: 4, 7, 10, 13, …?

  Use the nth term formula for AS
• What is the nth term formula for an arithmetic sequence?

  $a_n =$$a_1 +$$(n - 1) \times d$
• What does \(a_n\) represent in the nth term formula?

  The nth term of the sequence
• What does \(d\) represent in the nth term formula?

  The common difference of the sequence
• How do you find the nth term of the sequence: -4, -1, 2, 5, …?

  Use the nth term formula for AS
• What is the formula to find the sum of the first n terms of an arithmetic sequence?

  $S_n =$$\frac{n}{2} \times (a_1 + a_n)$
• What does \(S_n\) represent in the sum formula?

  The sum of the first n terms
• How do you find the sum of the first 20 terms of the sequence: 2, 5, 8, 11, …?

  Use the sum formula for AS
• What is the Pythagorean Theorem?

  $c^2 =$$a^2 +$$b^2$
• What does \(c\) represent in the Pythagorean Theorem?

  The length of the hypotenuse
• How can you test if a triangle is right-angled?

  Check if \(c^2 = a^2 + b^2\)
• How do you find an unknown side in a right-angled triangle?

  Use the Pythagorean Theorem
• What is the distance formula in 3D?

  $d =$ \sqrt{(x_2 - x_1)^2 +$(y_2 - y_1)^2 +$ (z_2 - z_1)^2}
• How do you find the distance between the points (3, 4, 5) and (6, 8, 10)?

  Use the distance formula in 3D
• What is the distance formula in 2D?

  $d =$ \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
• How do you find the distance between the points (1, 2) and (4, 6)?

  Use the distance formula in 2D
• What is sine in a right-angled triangle?

  $\sin \theta =$$\frac{\text{opposite}}{\text{hypotenuse}}$
• What is cosine in a right-angled triangle?

  $\cos \theta =$$\frac{\text{adjacent}}{\text{hypotenuse}}$
• What is tangent in a right-angled triangle?

  $\tan \theta =$$\frac{\text{opposite}}{\text{adjacent}}$
• How do you find the opposite side if the angle is 30° and the hypotenuse is 10 cm?

  Use sine function
• How do you find the hypotenuse if the angle is 45° and the adjacent side is 7 cm?

  Use cosine function
• How do you find an angle using inverse functions?

  Use \(\sin^{-1}\), \(\cos^{-1}\), or \(\tan^{-1}\)
• What is the formula for finding an angle using sine?

  $\theta =$$\sin^{-1} \left( \frac{\text{opposite}}{\text{hypotenuse}} \right)$
• What is the formula for finding an angle using cosine?

  $\theta =$$\cos^{-1} \left( \frac{\text{adjacent}}{\text{hypotenuse}} \right)$
• What is the formula for finding an angle using tangent?

  $\theta =$$\tan^{-1} \left( \frac{\text{opposite}}{\text{adjacent}} \right)$
• How do you solve multi-stage problems using trigonometric ratios?

  Break the problem into steps
• What is the angle of elevation?

  The angle when looking up at an object
• What is the angle of depression?

  The angle when looking down at an object
• How do you find the height of a tower using the angle of elevation?

  Use trigonometric ratios
• How do you find the height of a flagpole using the angle of depression?

  Use trigonometric ratios