Daily Practice · Higher Plus
January 2006 - Higher Plus 5-a-day
Every Higher Plus sheet published in January 2006, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' January 2006 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in January 2006
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st January 2006f(x) = 7x - 1. Work out the inverse function f^-1(x).
- 2nd January 2006A train slows steadily from 18 m/s to rest in 10 seconds. Work out its deceleration.
- 3rd January 2006A cuboid measures 14 cm by 13 cm by 13 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 4th January 2006A bag holds 6 red, 3 blue and 5 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 5th January 2006A histogram has two bars: one 10 units wide with frequency density 0.4, one 5 units wide with density 3. How many values in total?
- 6th January 2006Rationalise the denominator of 49/sqrt(7), giving your answer in its simplest form.
- 7th January 2006Solve x^2 + y^2 = 25 and y = x - 1 simultaneously.
- 8th January 2006y is inversely proportional to x^2. When x = 3, y = 64. Work out y when x = 4.
- 9th January 2006The point (20, 21) lies on the circle x^2 + y^2 = 841. Work out the gradient of the tangent to the circle at that point.
- 10th January 2006A bag holds 6 counters, r of them red. Two are taken without replacement and P(both red) = 2/5. Work out r.
- 11th January 2006On a histogram, a 5-wide bar and a 20-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 12th January 2006Simplify sqrt(18) + sqrt(18), giving your answer in the form a sqrt(b).
- 13th January 2006Use the iteration x(n+1) = cube root of (11x(n) + 5) with x(0) = 1. Work out x(1) to 3 decimal places.
- 14th January 2006y is directly proportional to x^3. When x = 2, y = 40. Work out y when x = 3.
- 15th January 2006In a circle theorem proof, a step uses the fact that two tangents are drawn to a circle from the same external point. State the reason being quoted.
- 16th January 2006The probability of winning a game is 1/2. A player expects 28 wins. How many games did they play?
- 17th January 2006A histogram has two bars: one 20 units wide with frequency density 1.5, one 20 units wide with density 1.4. How many values in total?
- 18th January 2006A rectangle is 14 cm by 8 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 19th January 2006Work out the nth term of the quadratic sequence 1, 8, 23, 46, ...
- 20th January 2006y is directly proportional to sqrt(x). When x = 4, y = 14. Work out y when x = 36.
- 21st January 2006In a vector proof you find that vector PQ = 2a - 4b and vector RS = 4a - 8b. What does this show about PQ and RS?
- 22nd January 2006A bag holds 3 red and n blue counters. The probability of taking a red is 1/2. Work out n.
- 23rd January 2006On a histogram, a 5-wide bar and a 20-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 24th January 2006Expand and simplify (9 + sqrt(11))(9 - sqrt(11)).
- 25th January 2006The point (4, 1) lies on y = f(x). Write down its image on y = f(x) + 3.
- 26th January 2006A train slows steadily from 22 m/s to rest in 8 seconds. Work out its deceleration.
- 27th January 2006A cuboid measures 4 cm by 15 cm by 6 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 28th January 2006A bag holds 5 red and 5 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 29th January 2006A histogram has two bars: one 20 units wide with frequency density 2.5, one 10 units wide with density 1.4. How many values in total?
- 30th January 2006A block has mass 440 g (to the nearest 10 g) and volume 8 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 31st January 2006Prove that the sum of 7 consecutive integers is always a multiple of 7. State the simplified sum you would use.