Daily Practice · Higher Plus
July 2007 - Higher Plus 5-a-day
Every Higher Plus sheet published in July 2007, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' July 2007 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in July 2007
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st July 2007f(x) = 5x + 1 and g(x) = 3x - 4. Work out fg(3).
- 2nd July 2007y is directly proportional to sqrt(x). When x = 4, y = 10. Work out y when x = 36.
- 3rd July 2007The point (5, 12) lies on the circle x^2 + y^2 = 169. Work out the gradient of the tangent to the circle at that point.
- 4th July 2007A bag holds 9 counters, r of them red. Two are taken without replacement and P(both red) = 1/36. Work out r.
- 5th July 2007On a histogram, a 10-wide bar and a 20-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 6th July 2007Rationalise the denominator of 18/sqrt(2), giving your answer in its simplest form.
- 7th July 2007The curve y = sin x° is drawn for 0 <= x <= 360. Write down the value of y when x = 270.
- 8th July 2007A train slows steadily from 35 m/s to rest in 10 seconds. Work out its deceleration.
- 9th July 2007In a circle theorem proof, a step uses the fact that the alternate segment theorem is being proved. State the reason being quoted.
- 10th July 2007The probability of winning a game is 1/5. A player expects 10 wins. How many games did they play?
- 11th July 2007A histogram has two bars: one 20 units wide with frequency density 1.2, one 20 units wide with density 3.5. How many values in total?
- 12th July 2007Simplify sqrt(32) + sqrt(8), giving your answer in the form a sqrt(b).
- 13th July 2007A quadratic sequence starts 0, 3, 10, 21. Work out the second difference, and the coefficient of n^2.
- 14th July 2007y is inversely proportional to x^2. When x = 3, y = 4. Work out y when x = 2.
- 15th July 2007In a vector proof you find that vector PQ = 2a - 6b and vector RS = 6a - 18b. What does this show about PQ and RS?
- 16th July 2007A bag holds 5 red and n blue counters. The probability of taking a red is 5/11. Work out n.
- 17th July 2007On a histogram, a 10-wide bar and a 30-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 18th July 2007A rectangle is 13 cm by 18 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 19th July 2007Solve x^2 - 7x + 6 < 0.
- 20th July 2007y is directly proportional to x^3. When x = 3, y = 135. Work out y when x = 5.
- 21st July 2007A cuboid measures 5 cm by 9 cm by 11 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 22nd July 2007A bag holds 3 red and 11 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 23rd July 2007A histogram has two bars: one 20 units wide with frequency density 1.2, one 5 units wide with density 0.8. How many values in total?
- 24th July 2007Expand and simplify (9 + sqrt(2))(9 - sqrt(2)).
- 25th July 2007Write x^2 - 16x + 6 in the form (x + a)^2 + b.
- 26th July 2007y is directly proportional to sqrt(x). When x = 9, y = 24. Work out y when x = 64.
- 27th July 2007A cuboid measures 12 cm by 9 cm by 10 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 28th July 2007A bag holds 5 red, 3 blue and 3 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 29th July 2007On a histogram, a 10-wide bar and a 20-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 30th July 2007A block has mass 500 g (to the nearest 10 g) and volume 23 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 31st July 2007Work out the coordinates of the turning point of y = x^2 + 14x - 1.