Daily Practice · Higher Plus
January 2014 - Higher Plus 5-a-day
Every Higher Plus sheet published in January 2014, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' January 2014 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in January 2014
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st January 2014Work out the coordinates of the turning point of y = x^2 - 8x - 10.
- 2nd January 2014y is directly proportional to sqrt(x). When x = 4, y = 14. Work out y when x = 16.
- 3rd January 2014In a circle theorem proof, a step uses the fact that two angles at the circumference stand on the same arc. State the reason being quoted.
- 4th January 2014The probability of winning a game is 2/5. A player expects 16 wins. How many games did they play?
- 5th January 2014On a histogram, a 10-wide bar and a 40-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 6th January 2014A block has mass 650 g (to the nearest 10 g) and volume 25 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 7th January 2014Simplify (x^2 - 6x - 16)/(x - 8).
- 8th January 2014A train slows steadily from 36 m/s to rest in 8 seconds. Work out its deceleration.
- 9th January 2014In a vector proof you find that vector PQ = 4a + 2b and vector RS = 20a + 10b. What does this show about PQ and RS?
- 10th January 2014A bag holds 2 red and n blue counters. The probability of taking a red is 1/5. Work out n.
- 11th January 2014A histogram has two bars: one 5 units wide with frequency density 2, one 25 units wide with density 3. How many values in total?
- 12th January 2014x = 196 and y = 108, each correct to the nearest whole number. Work out the upper bound of x - y.
- 13th January 2014In an algebraic proof, how would you write the product of two consecutive integers in terms of an integer n?
- 14th January 2014y is inversely proportional to x^2. When x = 5, y = 16. Work out y when x = 2.
- 15th January 2014A cuboid measures 8 cm by 4 cm by 5 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 16th January 2014A bag holds 4 red and 4 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 17th January 2014On a histogram, a 10-wide bar and a 30-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 18th January 2014A car covers 150 m (to the nearest 10 m) in 7 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 19th January 2014Make x the subject of 6x + 3 = y(x + 3).
- 20th January 2014y is directly proportional to x^3. When x = 2, y = 40. Work out y when x = 4.
- 21st January 2014A cuboid measures 6 cm by 7 cm by 11 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 22nd January 2014A bag holds 3 red, 7 blue and 5 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 23rd January 2014A histogram has two bars: one 10 units wide with frequency density 1.5, one 25 units wide with density 0.6. How many values in total?
- 24th January 2014Rationalise the denominator of 30/sqrt(5), giving your answer in its simplest form.
- 25th January 2014Write 4/(x + 2) + 2/(x - 6) as a single fraction.
- 26th January 2014y is directly proportional to sqrt(x). When x = 4, y = 16. Work out y when x = 81.
- 27th January 2014The point (12, 16) lies on the circle x^2 + y^2 = 400. Work out the gradient of the tangent to the circle at that point.
- 28th January 2014A bag holds 9 counters, r of them red. Two are taken without replacement and P(both red) = 7/12. Work out r.
- 29th January 2014On a histogram, a 5-wide bar and a 15-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 30th January 2014Simplify sqrt(32) + sqrt(8), giving your answer in the form a sqrt(b).
- 31st January 2014Solve 15x^2 + 8x - 12 = 0.