Daily Practice · Higher Plus
April 2010 - Higher Plus 5-a-day
Every Higher Plus sheet published in April 2010, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' April 2010 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.
Every sheet in April 2010
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st April 2010A bag holds 5 red and n blue counters. The probability of taking a red is 1/2. Work out n.
- 2nd April 2010A histogram has two bars: one 20 units wide with frequency density 2.5, one 5 units wide with density 3. How many values in total?
- 3rd April 2010A car covers 620 m (to the nearest 10 m) in 5 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 4th April 2010The point (-5, 4) lies on y = f(x). Write down its image on y = f(x) + 1.
- 5th April 2010y is directly proportional to sqrt(x). When x = 49, y = 35. Work out y when x = 9.
- 6th April 2010A cuboid measures 9 cm by 14 cm by 4 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 7th April 2010A bag holds 10 red and 4 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 8th April 2010On 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?
- 9th April 2010Rationalise the denominator of 36/sqrt(3), giving your answer in its simplest form.
- 10th April 2010Prove that the sum of 5 consecutive integers is always a multiple of 5. State the simplified sum you would use.
- 11th April 2010A train slows steadily from 34 m/s to rest in 5 seconds. Work out its deceleration.
- 12th April 2010A cuboid measures 9 cm by 6 cm by 14 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 13th April 2010A bag holds 3 red, 3 blue and 2 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 14th April 2010A histogram has two bars: one 5 units wide with frequency density 0.4, one 25 units wide with density 1.4. How many values in total?
- 15th April 2010Simplify sqrt(75) + sqrt(147), giving your answer in the form a sqrt(b).
- 16th April 2010f(x) = 5x - 8 and g(x) = 3x + 6. Work out fg(-1).
- 17th April 2010y is inversely proportional to x^2. When x = 5, y = 8. Work out y when x = 2.
- 18th April 2010The 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.
- 19th April 2010A bag holds 9 counters, r of them red. Two are taken without replacement and P(both red) = 1/6. Work out r.
- 20th April 2010On 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?
- 21st April 2010A rectangle is 22 cm by 11 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 22nd April 2010The curve y = cos x° is drawn for 0 <= x <= 360. Write down the value of y when x = 270.
- 23rd April 2010y is directly proportional to x^3. When x = 4, y = 256. Work out y when x = 5.
- 24th April 2010In a circle theorem proof, a step uses the fact that a triangle is drawn from the ends of a diameter to a point on the circle. State the reason being quoted.
- 25th April 2010The probability of winning a game is 1/5. A player expects 9 wins. How many games did they play?
- 26th April 2010A histogram has two bars: one 5 units wide with frequency density 0.4, one 10 units wide with density 3. How many values in total?
- 27th April 2010Expand and simplify (4 + sqrt(6))(4 - sqrt(6)).
- 28th April 2010A quadratic sequence starts 1, 9, 25, 49. Work out the second difference, and the coefficient of n^2.
- 29th April 2010y is directly proportional to sqrt(x). When x = 4, y = 14. Work out y when x = 16.
- 30th April 2010In a vector proof you find that vector PQ = 2a + 6b and vector RS = 6a + 18b. What does this show about PQ and RS?