Daily Practice · Higher Plus
January 2013 - Higher Plus 5-a-day
Every Higher Plus sheet published in January 2013, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' January 2013 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in January 2013
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st January 2013y is directly proportional to x^3. When x = 3, y = 108. Work out y when x = 2.
- 2nd January 2013The point (8, 15) lies on the circle x^2 + y^2 = 289. Work out the gradient of the tangent to the circle at that point.
- 3rd January 2013A bag holds 10 counters, r of them red. Two are taken without replacement and P(both red) = 1/3. Work out r.
- 4th January 2013A histogram has two bars: one 20 units wide with frequency density 1.5, one 5 units wide with density 1.4. How many values in total?
- 5th January 2013A car covers 320 m (to the nearest 10 m) in 8 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 6th January 2013Use the iteration x(n+1) = cube root of (5x(n) + 2) with x(0) = 1. Work out x(1) to 3 decimal places.
- 7th January 2013y is directly proportional to sqrt(x). When x = 36, y = 18. Work out y when x = 4.
- 8th January 2013In a circle theorem proof, a step uses the fact that OA and OB are both radii of the circle, so triangle OAB is isosceles. State the reason being quoted.
- 9th January 2013The probability of winning a game is 3/5. A player expects 18 wins. How many games did they play?
- 10th January 2013On a histogram, a 10-wide bar and a 30-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 11th January 2013Rationalise the denominator of 28/sqrt(7), giving your answer in its simplest form.
- 12th January 2013Work out the nth term of the quadratic sequence 9, 16, 25, 36, ...
- 13th January 2013A train slows steadily from 20 m/s to rest in 8 seconds. Work out its deceleration.
- 14th January 2013In a vector proof you find that vector PQ = 2a + 3b and vector RS = 4a + 6b. What does this show about PQ and RS?
- 15th January 2013A bag holds 7 red and n blue counters. The probability of taking a red is 7/9. Work out n.
- 16th January 2013A histogram has two bars: one 5 units wide with frequency density 1.2, one 20 units wide with density 3.5. How many values in total?
- 17th January 2013Simplify sqrt(8) + sqrt(98), giving your answer in the form a sqrt(b).
- 18th January 2013The point (5, -2) lies on y = f(x). Write down its image on y = f(x) - 3.
- 19th January 2013y is inversely proportional to x^2. When x = 2, y = 50. Work out y when x = 5.
- 20th January 2013A cuboid measures 6 cm by 5 cm by 9 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 21st January 2013A bag holds 6 red and 7 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 22nd January 2013On a histogram, a 5-wide bar and a 10-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 23rd January 2013A rectangle is 21 cm by 4 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 24th January 2013Prove that the sum of 6 consecutive integers is always a multiple of 3. State the simplified sum you would use.
- 25th January 2013y is directly proportional to x^3. When x = 4, y = 128. Work out y when x = 3.
- 26th January 2013A cuboid measures 13 cm by 12 cm by 4 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 27th January 2013A bag holds 6 red, 5 blue and 3 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 28th January 2013A histogram has two bars: one 20 units wide with frequency density 1.5, one 10 units wide with density 0.6. How many values in total?
- 29th January 2013Expand and simplify (7 + sqrt(5))(7 - sqrt(5)).
- 30th January 2013f(x) = 2x - 5 and g(x) = 3x + 4. Work out fg(6).
- 31st January 2013y is directly proportional to sqrt(x). When x = 36, y = 54. Work out y when x = 49.